If A and B are two square matrices such that $B = - A^{- 1} B A$ , then $(A + B)^{2}$ is equal to

0

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A^{2} + B^{2}

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A^{2} + 2 A B + B^{2}

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A + B

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Solution

The correct option is B $A^{2} + B^{2}$
As $B = - A^{- 1} B A$ , we get AB = -BA or AB + BA = 0.
Now,
$(A + B)^{2} = (A + B) (A + B)$
$= A^{2} + B A + A B + B^{2}$
$= A^{2} + O + B^{2}$
$= A^{2} + B^{2}$ .

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Similar questions

B = - A^{- 1} B A

(A + B)^{2} = A^{2} + B^{2}

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

A

B

B = - A^{- 1} B A,

(A + B)^{2}

B = - A^{- 1} B A,

(A + B)^{2}

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