Equivalent statements to matrix A is orthogonal

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A is orthogonal if the A^{-1} = A^{T}.

Thus, AA^{T} = I.

However, is the statement A is orthogonal equivalent to A^{2}=I.

I don't think the statements are equivalent, but it comes from a test. Thus, I'd hope the test is correct.
 
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Multiply both sides of the A^2=I expression by A^-1 and see what you get.

From that expression you will be able to see the relationship required for both to be true.
 

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