The matrix set is
\begin{bmatrix} 1 & 1 \\ -1 &-1 \\ \end{bmatrix} \begin{bmatrix} 2 & -2 \\ -2 &2 \\ \end{bmatrix} \begin{bmatrix} 3 & -3 \\ 3 & -3 \\ \end{bmatrix}
I know that a set of nonzero vectors $\{ u_1, u_2,\cdots,u_m \}$ is called orthogonal if $u_i \cdot u_j = 0$ whenever $i \neq j$. It was insisted that this is an orthogonal set but when the formula is applied to the first and last matrix it yields: \begin{bmatrix} 6 & -6 \\ -6 & 6 \\ \end{bmatrix} which doesn't satisfy the $u_i \cdot u_j = 0$ condition. Am I doing something wrong? or it really isn't an orthogonal set.
Moreover, can I say that this is also an orthonormal set since an orthogonal set is automatically an orthonormal set? Thanks!