$A$ is a square matrix with $A^2 = A$ . What is $(I - A)^2$ ?

I - A

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I + A

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I - 2A

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I

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Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$(I - A)^2 = I - IA - AI + A^2 = I - 2A + A^2$ , because $I$ commutes with every matrix.
With $A^2 = A$ , this is $I - 2A + A = I - A$ .

Worth noting

$I - 2A$ stops before replacing $A^2$ by $A$ .

Ten questions from Matrices, at your own pace.

Ten questions from Matrices, at your own pace.

AAA is a square matrix with A2=AA^2 = AA2=A. What is (I−A)2(I - A)^2(I−A)2?