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If ‘A’ is a square matrix such that $A^{2} = A$ , then ${(I + A)}^{3} - 7 A$ is equal to

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$I - A$

$3 A$

$I$

$A$

answer is C.

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Detailed Solution

${(I + A)}^{3} - 7 A = I^{3} + A^{3} + 3 A + 3 A^{2} - 7 A$

$= I + A + 3 A + 3 A - 7 A$

$= I + 7 A - 7 A = I$

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