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Maths-

General

Easy

Question

If A and B are square matrices such that AB = B and BA = A, then A² + B² is equal to-

2AB
2BA
A + B
AB

The correct answer is: A + B

We are given that A and B are square matrices such that AB = B and BA = A and we are asked to find what A2 + B2 is equal to
$A squared space plus space B squared space equals A A plus B B equals A left parenthesis B A right parenthesis space plus space B left parenthesis A B right parenthesis equals left parenthesis A B right parenthesis space A space plus space left parenthesis B A right parenthesis B equals B A plus A B equals A plus B$

Hence the correct answer is choice 3

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