$A$ is a square matrix with $A^2 = I$ . Which of the following is always equal to $A^{-1}$ ?

-A

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A

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I

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O

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Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Worth noting

$I$ is $A^{-1}$ only when $A$ itself is $I$ ; $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ also has $A^2 = I$ .

Ten questions from Matrices, at your own pace.

AAA is a square matrix with A2=IA^2 = IA2=I. Which of the following is always equal to A−1A^{-1}A−1?