QuestionConsider the inner product on $M_{22}$ defined by $<U, V>=u_{1} v_{1}+u_{2} v_{2}+u_{3} v_{3}+u_{4} v_{4}$ where $U=\left[\begin{array}{ll}u_{1} & u_{2} \\ u_{3} & u_{4}\end{array}\right]$ and $V=\left[\begin{array}{ll}v_{1} & v_{2} \\ v_{3} & v_{4}\end{array}\right]$. Using this inner product, the matrices $\left[\begin{array}{ll}-1 & 47 \\ -5 & 5\end{array}\right]$ and $\left[\begin{array}{cc}2 & 1 \\ 5 & -4\end{array}\right]$ are orthogonal.
True False