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

A

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I - A

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I

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3 A

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Solution

The correct option is B $I$
${(I + A)}^{3} - 7 A = I^{3} + A^{3} + 3 I^{2} A + 3 A^{2} I - 7 A$
$= I + A^{3} + 3 A + 3 A^{2} - 7 A$
$= I + A^{2} . A + 3 A + 3 A - 7 A, [∵ A^{2} = A]$
$= I + A . A - A$
$= I + A^{2} - A$
$= I + A - A = I$
$∴ {(I + A)}^{3} - 7 A = I$

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Similar questions

If A is square matrix such that then is equal to

A. A B. I − A C. I D. 3A

A

A^{2} = A

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

A^{2} = A

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

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