Math Help - Orthonormal

1. Orthonormal

Could anyone help me with one direction proof of this problem please?

Suppose that beta and gamma are ordered bases for an n-dimensional real (complex) inner product space V. Prove that if Q is an orthogonal (unitary) n by n matrix that changes gamma-coordinates into beta-coordinates, then beta is orthonormal if and only if gamma is orthonormal.

2. Hint: for vectors x, y in V, $\langle Qx,Qy\rangle = \langle Q^*Qx,y\rangle = \langle x,y\rangle$.