Thread: Orthogonal Matrices and the dot product

If A is an n x n real matrix, how would I start each part of a proof that A is an orthogonal matrix iff Ax dot Ay = x dot y for all x and y in Rn?

start with the fact that , where the right-hand side is a matrix product of a 1xn and an nx1 matrix.

Thanks so much! I think I got. I used the fact that A^-1 = A^t iff A is an orthogonal matrix!

Thank you again!