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CBSE Class 12-science Answered

A,B are two matrices such that AB and A+B are both defined; show that A,B are square matrices of the same order.
Asked by azizrajil03 | 13 Apr, 2019, 11:40: AM
answered-by-expert Expert Answer
F o r space a d d i t i o n space t o space b e space d e f i n e d space f o r space t w o space m a t r i c e s comma space i t space i s space c o m p u l s o r y space t h a t space t h e i r space o r d e r s space a r e space s a m e L e t space A space b e space a n space m cross times n space m a t r i x space a n d space B space b e space a n space p cross times q space m a t r i x N o w space sin c e space t h e space a d d i t i o n space A plus B space i s space d e f i n e d comma space t h e n space w e space h a v e m equals p space a n d space n equals q space............ space left parenthesis i right parenthesis N o w comma space f o r space m u l t i p l i c a t i o n space o f space m a t r i c e s space t o space d e f i n e d space i t space i s space c o m p u l s o r y space t h a t space t h e space c o l u m n space n u m b e r space o f space 1 s t space m a t r i x space i s space s a m e space a s space t h e space r o w space n u m b e r space o f space s e c o n d space m a t r i x S o comma space w e space h a v e n equals p A n d space u sin g space left parenthesis i right parenthesis comma space w e space h a v e m equals n space a n d space p equals q T h u s comma space t h e space o r d e r space m a t r i x space A space a n d space B space a r e space s q u a r e space m a t r i c e s.
Answered by Renu Varma | 14 Apr, 2019, 03:50: PM

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