i have a linera algebra quiz on this proof tomorrow so if anyone could show me how the following is done, i would be really thankful...

An orthogonal matrix is one for which A^T = A^-1 (meaning A transpose = inverse of A).

Prove that if a matrix A is orthogonal, then any two distinct columns of A have dot product zero.

Is this true for the converse of this statement as well? Justify your answer.