If A and B are two matrices such that AB = B and BA = A, then A^2… - Vidyadip

MCQ

If $A$ and $B$ are two matrices such that $AB = B$ and $BA = A,$ then ${A^2} + {B^2} = $

A
$2AB$
B
$2BA$
✓
$A + B$
D
$AB$

✓

Answer

Correct option: C.

$A + B$

c
(c) We have $AB = B$ and $BA = A$.

Therefore ${A^2} + {B^2} = AA + BB = A(BA) + B(AB)$

$ = (AB)A + (BA)B = BA + AB = A + B$,

$(\because \,\,AB = B$ and $BA = A)$.

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