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

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 C $A + B$
Given,
$A B = B$
and
$B A = A$
Now,
$A^{2} + B^{2} = A \cdot A + B \cdot B$
$= A (B A) + B (A B) = (A B) A + (B A) B$
$= B A + A B = A + B$

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Similar questions

A

B

A B = B

B A = A

A^{2} + B^{2}

A B = B

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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