# Equivalent statements to matrix A is orthogonal

1. Sep 17, 2013

### CAVision

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.

2. Sep 17, 2013

### UltrafastPED

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.