# Equivalent statements to matrix A is orthogonal

## Main Question or Discussion Point

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.