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

3 I

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O

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I

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2 I

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Solution

The correct option is D $I$
Given $A^{2} = A$

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

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

$= I + 7 A - 7 A$

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

Suggest Corrections

Similar questions

A

A^{2} = A

{(I + A)}^{3} - 7 A

If A is square matrix such that then is equal to

A. A B. I − A C. I D. 3A

A^{2} = A

7 A - {(I + A)}^{3}

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