Here's the question: Let Q be a square $n\times n$ matrix. Let $\{{\mathbf{\text{e}}}_{1},{\mathbf{\text{e}}}_{2},...,{\mathbf{\text{e}}}_{n}\}$ be the n standard basis column vectors of Rn. Show that the set of vectors $\{Q{\mathbf{\text{e}}}_{1},Q{\mathbf{\text{e}}}_{2},...,Q{\mathbf{\text{e}}}_{n}\}$ also form a set of orthonormal vectors.

In terms of my attempts, I've proven that each column vector of Q forms a set of orthonormal vectors in ${\mathbb{R}}^{n}$. I feel like this may be very close but I'm struggling to picture where to go from here. If this method is correct, where do I go from here? If this method is not correct, what would be the best way to prove this?

In terms of my attempts, I've proven that each column vector of Q forms a set of orthonormal vectors in ${\mathbb{R}}^{n}$. I feel like this may be very close but I'm struggling to picture where to go from here. If this method is correct, where do I go from here? If this method is not correct, what would be the best way to prove this?