## Related questions with answers

Question

Determine whether the statements that follow are true or false, and justify your answer: If $A^2 = I_2$, then matrix $A$ must be either $I_2$ or $-I_2$.

Solution

VerifiedStep 1

1 of 2If

$A=\begin{bmatrix} 1&0 \\ 0&-1 \end{bmatrix}$

, then $A^2=I_2$, but $A$ is neither $I_2$ nor $-I_2$.

Statement is false.

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