SELINA Solutions for Class 10 Maths Chapter 9 - Matrices
Practise Selina Solutions for ICSE Class 10 Mathematics Chapter 9 Matrices to revise chapter concepts easily. Learn to write the additive inverse of the given matrices. Understand concepts such as the order of a matrix, multiplication of a matrix, identity matrices etc. by using our online learning resources.
Learn whether the given addition or subtraction of matrices is commutative or not commutative in the textbook questions. You may also revise the ‘True or False’ type questions from the Selina textbook through our ICSE Class 10 Maths solutions. Further, TopperLearning enables self-paced learning by giving you access to video lessons, practice tests and previous years’ question papers.
Chapter 9 - Matrices Exercise Ex. 9(A)
Question 1
State, whether the following statements are true or false. If false, give a reason.
(i) If A and B are
two matrices of orders 3 
2 and 2 3 respectively; then their sum A + B is possible.
(ii) The matrices 
and 
are conformable for subtraction.
(iii) Transpose of a
2 1 matrix is a 2 1 matrix.
(iv) Transpose of a square matrix is a square matrix.
(v) A column matrix has many columns and one row.
Solution 1
(i) False
The sum A + B is possible when the order of both the matrices A and B are same.
(ii) True
(iii) False
Transpose of a 2 1 matrix is a 1 2 matrix.
(iv) True
(v) False
A column matrix has only one column and many rows.
Question 2
Given: 
, find x, y and z.
Solution 2
If two matrices are equal, then their corresponding elements are also equal. Therefore, we have:
x = 3,
y + 2 = 1 
y = -1
z - 1 = 2 z = 3
Question 3
Solve for a, b and c if
(i) 
(ii) 
Solution 3
If two matrices are equal, then their corresponding elements are also equal.
(i)
a + 5 = 2 
a = -3
-4 = b + 4 b = -8
2 = c - 1 c = 3
(ii) a= 3
a - b = -1
b = a + 1 = 4
b + c = 2
c = 2 - b = 2 - 4 = -2
Question 4
If A =
and B = 
; find: (i) A + B (ii) B - A
Solution 4
(i) A + B =
(ii) B - A 
Question 5
If A=
, B = 
and C = 
; find:
(i) B + C (ii) A - C
(iii) A + B - C (iv) A - B +C
Solution 5
(i)B + C = 
(ii)A - C = 
(iii)A + B - C =
=
= 
(iv)A - B +C =
=
= 
Question 6
Wherever possible, write each of the following as a single matrix.
(i) 
(ii) 
(iii) 
Solution 6
(i) 
(ii) 
(iii) Addition is not possible, because both matrices are not of same order.
Question 7
Find, x and y from the following equations :
Solution 7
(i)
Equating the corresponding elements, we get,
3 - x = 7 and y + 2 = 2
Thus, we get, x = - 4 and y = 0.
(ii)
Equating the corresponding elements, we get,
-8 + y = -3 and x - 2 =2
Thus, we get, x = 4 and y = 5.
Question 8
Given: M =
, find its transpose matrix Mt.
If possible, find:
(i) M + Mt (ii) Mt - M
Solution 8
M =
Mt = 
(i) 
(i) 
Question 9
Write the additive inverse of matrices A, B and C:
Where 
Solution 9
We know additive inverse of a matrix is its negative.
Additive inverse of A = 
Additive inverse of B = 
Additive inverse of C = 
Question 10
Given 
; find the matrix X in each of the following:
(i) X + B = C - A
(ii) A - X = B + C
Solution 10
(i) X + B = C - A
(ii) A - X = B + C
Question 11
Given 
; find the matrix X in each of the following:
(i) A + X = B
(ii) A - X = B
(iii) X - B = A
Solution 11
(i) A + X = B
X = B - A
(ii) A - X = B
X = A - B
(iii) X - B = A
X = A + B
Chapter 9 - Matrices Exercise Ex. 9(B)
Question 1
Evaluate:
Solution 1
Question 2
Find x and y if:
Solution 2
Comparing the corresponding elements, we get,
12 + 2y = 10 and 3x - 6 = 0
Simplifying, we get, y = -1 and x = 2.
Comparing corresponding the elements, we get,
-x + 8 = 7 and 2x - 4y = -8
Simplifying, we get,
x = 1 and y = 
= 2.5
Question 3
Given 
; find:
(i) 2A - 3B + C
(ii) A + 2C - B
Solution 3
(i) 2A - 3B + C
(ii) A + 2C - B
Question 4
Solution 4
Question 5
Given 
(i) find the matrix 2A + B
(ii) find the matrix C such that:
C + B = 
Solution 5
(i)
(ii)
C + B =
C
= - B = 
Question 6
If 
; find the
values of x, y and z.
Solution 6
Comparing the corresponding elements, we get,
2x
+ 9 = -7 
2x = -16 x = -8
3y
= 15 y = 5
z = 9
Question 7
Given A = 
and At
is its transpose matrix. Find:
(i) 2A + 3At (ii) 2At - 3A
(iii) 
(iv)
Solution 7
(i) 2A + 3At
(ii) 2At - 3A
(iii)
(iv)
Question 8
Given 
Solve for matrix X:
(i) X + 2A = B
(ii) 3X + B + 2A = O
(iii) 3A - 2X = X - 2B.
Solution 8
(i) X + 2A = B
X = B - 2A
(ii) 3X + B + 2A = O
3X = -2A - B
(iii) 3A - 2X = X - 2B
3A + 2B = X + 2X
3X = 3A + 2B
Question 9
If 
, show that:
3M + 5N = 
Solution 9
3M + 5N
Question 10
If I is the unit matrix of order 2 x 2; find the matrix M, such that:
(i) M - 2I = 
(ii) 5M + 3I = 
Solution 10
(i)
M - 2I =
(ii)
5M + 3I =
Question 11
If 
Solution 11
2M = 
M = 
Chapter 9 - Matrices Exercise Ex. 9(C)
Question 1
Evaluate: if possible:
Solution 1
The number of columns in the first matrix is not equal to the number of rows in the second matrix. Thus, the product is not possible.
Question 2
If 
and I is a
unit matrix of order 2 
2, find:
(i) AB (ii) BA (iii) AI
(iv) IB (v) A2 (vi) B2A
Solution 2
Question 3
Solution 3
Question 4
Find x and y, if:
Solution 4
Comparing the corresponding elements, we get,
5x
- 2 = 8 
x = 2
20
+ 3x = y y = 20 + 6 =
26
Comparing the corresponding elements, we get,
x = 2
-3
+ y = -2 y = 1
Question 5
If 
, find:
(i) (AB)C (ii) A(BC)
Is A(BC) = (AB)C?
Solution 5
Hence, A(BC) = (AB)C.
Question 6
Given 
, find; if
possible:
(i) AB (ii) BA (iii)A2
Solution 6
(iii) Product AA (=A2) is not possible as the number of columns of matrix A is not equal to its number of rows.
Question 7
Solution 7
Question 8
If M = 
and I is a unit matrix of the same order as that of M; show that:
M2 = 2M + 3I
Solution 8
Hence, M2 = 2M + 3I.
Question 9
If 
and BA= M2, find the values of a and b.
Solution 9
Given, BA = M2
Comparing the corresponding elements, we get,
a = 2 and -2b = -2 
b = 1
Question 10
Given 
, find:
(i) A - B (ii) A2
(iii) AB (iv) A2 - AB + 2B
Solution 10
Question 11
If 
; find:
(i) (A + B)2 (ii) A2 + B2
(iii) Is (A + B)2 = A2 + B2?
Solution 11
(iii)
Clearly, (A + B)2 
A2
+ B2
Question 12
Find the matrix A, if B =
and B2
= B + 
A.
Solution 12
B2
= B + A
A = B2
- B
A = 2(B2 - B)
Question 13
If A = 
and A2 = I; find a and b.
Solution 13
It is given that A2 = I.
Comparing the corresponding elements, we get,
1 + a = 1
Therefore, a = 0
-1 + b = 0
Therfore, b = 1
Question 14
If 
; then show
that:
(i) A (B + C) = AB + AC
(ii) (B - A)C = BC - AC.
Solution 14
Question 15
If 
, simplify:
A2 + BC.
Solution 15
Question 16(i)
Solve for x and y:
Solution 16(i)
Question 16(ii)
Solve for x and y:
Solution 16(ii)
Question 16(iii)
Solution 16(iii)
Question 17
In each case given below, find:
(a) The order of matrix M.
(b) The matrix M.
Solution 17
We know, the product of two matrices is defined only when the number of columns of first matrix is equal to the number of rows of the second matrix.
(i) Let the order of matrix M be a x b.
Clearly, the order of matrix M is 1 x 2.
Comparing the corresponding elements, we get,
a = 1 and a + 2b = 2 
2b = 2 - 1 = 1 b = 
(ii) Let the order of matrix M be a x b.
Clearly, the order of matrix M is 2 x 1.
Comparing the corresponding elements, we get,
a + 4b = 13 ....(1)
2a + b = 5 ....(2)
Multiplying (2) by 4, we get,
8a + 4b = 20 ....(3)
Subtracting (1) from (3), we get,
7a = 7 a = 1
From (2), we get,
b = 5 - 2a = 5 - 2 = 3
Question 18
If 
; find the
value of x, given that: A2 = B.
Solution 18
Question 19
Solution 19
Question 20
If A and B are any two 2 x 2 matrices such that AB = BA = B and B is not a zero matrix, what can you say about the matrix A?
Solution 20
AB = BA = B
We know that I × B = B × I = B, where I is the identity matrix.
Hence, A is an identity matrix.
Question 21
Given 
and that AB = A + B; find the values of a, b and c.
Solution 21
Comparing the corresponding elements, we get,
3a = 3 + a
2a = 3
a = 
3b = b 
b = 0
4c = 4 + c 3c = 4 c = 
Question 22
If 
, then compute:
(i) P2 - Q2 (ii) (P + Q) (P - Q)
Is (P + Q) (P - Q) = P2 - Q2 true for matrix algebra?
Solution 22
Clearly, it can be said that:
(P + Q) (P - Q) = P2 - Q2 not true for matrix algebra.
Question 23
Given the matrices:
. Find:
(i) ABC (ii) ACB.
State whether ABC = ACB.
Solution 23
Hence, ABC ≠ ACB.
Question 24
If 
; find each of the following and state if they are equal:
(i) CA + B (ii) A + CB
Solution 24
Thus, CA + B 
A + CB
Question 25
If 
; find the matrix X such that AX = B.
Solution 25
Clearly, the order of matrix X is 2 x 1.
Comparing the two matrices, we get,
2x + y = 3 … (1)
x + 3y = -11 … (2)
Multiplying (1) with 3, we get,
6x + 3y = 9 … (3)
Subtracting (2) from (3), we get,
5x = 20
x = 4
From (1), we have:
y = 3 - 2x = 3 - 8 = -5
Question 26
If
, find (A - 2I)
(A - 3I).
Solution 26
Question 27
If 
, find:
(i) At. A (ii) A. At
Where At is the transpose of matrix A.
Solution 27
Question 28
If
, show that: 6M - M2 = 9I; where I is a 2 x 2 unit matrix.
Solution 28
Hence, proved.
Question 29
If
; find x and y such that PQ = null matrix.
Solution 29
Comparing the corresponding elements, we get,
2x + 12 = 0
thus, x = -6
6 + 6y = 0
thus, y = -1
Question 30
Evaluate without using tables:
Solution 30
Question 31
State, with reason, whether the following are true or false. A, B and C are matrices of order 2 x 2.
(i) A + B = B + A
(ii) A - B = B - A
(iii) (B. C). A = B. (C. A)
(iv) (A + B). C = A. C + B. C
(v) A. (B - C) = A. B - A. C
(vi) (A - B). C = A. C - B. C
(vii) A2 - B2 = (A + B) (A - B)
(viii) (A - B)2 = A2 - 2A. B + B2
Solution 31
(i) True.
Addition of matrices is commutative.
(ii) False.
Subtraction of matrices is not commutative.
(iii) True.
Multiplication of matrices is associative.
(iv) True.
Multiplication of matrices is distributive over addition.
(v) True.
Multiplication of matrices is distributive over subtraction.
(vi) True.
Multiplication of matrices is distributive over subtraction.
(vii) False.
Laws of algebra for factorization and expansion are not applicable to matrices.
(viii) False.
Laws of algebra for factorization and expansion are not applicable to matrices.
Chapter 9 - Matrices Exercise Ex. 9(D)
Question 1
Find x and y, if:
Solution 1
Comparing the corresponding elements, we get,
6x - 10 = 8
6x = 18
x = 3
-2x + 14 = 4y
4y = -6+ 14 = 8
y = 2
Question 2
Find x and y, if:
Solution 2
Comparing the corresponding elements, we get,
3x + 18 = 15
3x = -3
x = -1
12x + 77 = 10y
10y = -12 + 77 = 65
y = 6.5
Question 3
If 
; find x and y, if:
(i) x, y Î W (whole numbers)
(ii) x, y Î Z (integers)
Solution 3
(i) x, y Î W (whole numbers)
It can be observed that the above two equations are satisfied when x = 3 and y = 4.
(ii) x, y Î Z (integers)
It can be observed that the above two equations are satisfied when x = 
3 and y = 4.
Question 4
Solution 4
(i)
(ii)
Question 5
Evaluate:
Solution 5
Question 6
If
and 3A x M = 2B; find matrix M.
Solution 6
Let the order of matrix M be a x b.
3A x M = 2B
Clearly, the order of matrix M is 2 x 1.
Comparing the corresponding elements, we get,
-3y = -10
y = 
12x - 9y = 12
Question 7
If 
, find the values of a, b and c.
Solution 7
Comparing the corresponding elements, we get,
a + 1 = 5 
a = 4
2 + b = 0 b = -2
-1 - c = 3 c = -4
Question 8
If A = 
; find:
(i) A (BA)
(ii) (AB). B
Solution 8
(i)
(ii)
Question 9
Find x and y, if: 
Solution 9
Comparing the corresponding elements, we get,
5x = 5
x = 1
6y = 12 y = 2
Question 10
If matrix X =
and 2X - 3Y =
; find the matrix 'X' and 'Y'.
Solution 10
Question 11
Given 
; find the matrix X such that:
A + X = 2B + C
Solution 11
Given, A + X = 2B + C
Question 12
Find the value of x, given that A2 = B,
Solution 12
Given, A2 = B
Comparing the corresponding elements, we get,
x = 36
Question 13
If 
, and I is identity matrix of the same order and At is the transpose of matrix A, find At .B + BI
Solution 13
Question 14
Solution 14
Question 15
Let
. Find A2 - A + BC.
Solution 15
Question 16
Let A =
. Find A2 + AB + B2.
Solution 16
A =
A2 = A 
A = 
= 
AB = A B = 
=
= 
B2 = B x B = 
= 
= 
A2 + AB + B2 = 
= 
Question 17
If 
and 3A - 2C = 6B, find the values of a, b and c.
Solution 17
Comparing the corresponding elements, we get,
3a - 8 = 24 
3a = 32 a = 
24 - 2b = 0 2b = 24 b = 12
11 = 6c c = 
Question 18
Given A =
.
Find the values of p and q.
Solution 18
A = 
BA = 
C2 = 
BA = C2 
=
By comparing,
-2q = -8 q = 4
And p = 8
Question 19
Given A =
. Find AB + 2C - 4D.
Solution 19
AB = 
Question 20
Evaluate:
Solution 20
= 
= 
Question 21
Solution 21
Question 22
Solution 22
A2 = 9A + MI
⇒ A2 - 9A = mI ….(1)
Now, A2 = AA
Substituting A2 in (1), we have
A2 - 9A = mI
Question 23
(i) Write the order of matrix X.
(ii) Find the matrix 'X'
Solution 23
(i) Let the order of matrix X = m × n
Order of matrix A = 2 × 2
Order of matrix B = 2 × 1
Now, AX = B
∴ m = 2 and n = 1
Thus, order of matrix X = m × n = 2 × 1
Multiplying (1) by 2, we get
4x + 2y = 8 ….(3)
Subtracting (2) from (3), we get
3x = 3
⇒ x = 1
Substituting the value of x in (1), we get
2(1) + y = 4
⇒ 2 + y = 4
⇒ y = 2
Question 24
Find the matrix C where C is a 2 by 2 matrix.
Solution 24
Given: A2 - 5B2 = 5C
Question 25
Given matrix 
. Find the matrix X if, X = B2 - 4B. Hence,
solve for a and b given 
.
Solution 25
To find: a and b
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