CBSE Class 12-science Answered
2nd part of 14 ques
Asked by lovemaan5500 | 02 Jan, 2020, 08:54: PM
Expert Answer
The given set is {-1, 0, 1} and the binary operation is +
Now, -1+0=-1=0+-1, 1+0=1=0+1
Hence, the identity element for this set is e=0.
To find the inverse element
So, for an inverse b of an element a, it should satisfy
a+b=e=b+a
As the identity element is 0
Therefore, a+b=0=b+a
Therefore, for an element a, -a is its inverse element.
i.e. for -1, -1+1=0 so 1 is the inverse of -1
Similarly, 1+(-1)=0, so -1 is the inverse of 1.
And, for 0, 0 is inverse of itself.
Hence, the set has a unique inverse element for each element in the set.
Answered by Renu Varma | 03 Jan, 2020, 11:28: AM
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