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

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3 and 4 .Determinants and Matrices

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

A

$2AB$

B

$2BA$

C

$A + B$

D

$AB$

Solution

(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 $BA = A)$.

Standard 12

Mathematics

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