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Multiplication of Matrices

If A2=A, B2...

Question

If $A^{2} = A, B^{2} = B, A B = B A = O$ (Null Matrix), then $(A + B)^{2} =$

A - B

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A + B

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A^{2} - B^{2}

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0

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Solution

The correct option is B $A + B$
$(A + B)^{2} = A^{2} + B^{2} + A B + B A$
$= A + B$

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A = [\begin{matrix} 2 & - 1 0 & 1 \end{matrix}]

B = [\begin{matrix} 1 & 0 - 1 & - 1 \end{matrix}],

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

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