If A and B are two matrices such that $A B = B$ and $B A = A$ , then $A^{2} + B^{2}$ is equal to

2 A B

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2 B A

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A + B

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A B

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Solution

The correct option is D $A + B$
$A^{2} + B^{2} = A A + B B$
$= A (B A) + B (A B)$ (Given $A B = B a n d B A = A$ )
$= (A B) A + (B A) B$
$= B A + A B$
$= A + B$

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Similar questions

A

B

A B = B

B A = A

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A

B

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B A = A

A^{2} + B^{2}

Show that if A and B are square matrices such that AB = BA, then $(A + B)^{2} = A^{2} + 2 A B + B^{2}$ .

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