# Orthogonal and Orthonormal Matrix

I know that the columns of an orthogonal matrix are perpendicular to each other and additionally if the columns have unit length then they are orthonormal. But my professor states that the columns of an orthogonal matrix form an orthonormal basis? Is this right? Then what is the difference between orthogonal and orthonormal matrix?

• I've seen the term "orthonormal matrix" used to me a matrix whose columns are orthonormal vectors. So an orthonormal matrix $Q$ satisfies $Q^TQ = I$ but not necessarily $QQ^T = I$. Sep 8 '20 at 0:30
• if a matrix $A$ is orthogonal then $A^T$ is the inverse of $A$ which implies $A$$A^T= A^T$$A$ = I Sep 8 '20 at 0:41