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If $A^{2} = A,$ then $(A + I)^{4} - 16 A =$

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$I - A$

$I + A$

$I$

$A - I$

answer is A.

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Detailed Solution

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

$\begin{array}{ll} ∴ (A + I)^{4} = (3 A + I)^{2} = 9 A^{2} + 6 A + I = 15 A + I \\ ∴ (A + I)^{4} - 16 A = I - A \end{array}$

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