Exploit symmetries, \[{\begin{bmatrix} a & b \\ c & d \end{bmatrix}} \to \Bigg[ \begin{matrix} b & \\ a & d \\ c & \end{matrix}\]
\[\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} e & f \\ g & h \end{bmatrix} = \begin{bmatrix} ae+bg & af+bh \\ ce+dg & cf+dh \end{bmatrix} \to \Bigg[ \begin{matrix} af+bh & \\ ae+bg & cf+dh \\ ce+dg & \end{matrix}\]
\[\Bigg[ \begin{matrix} b & \\ a & d \\ c & \end{matrix}^T = \Bigg[\begin{matrix} c & \\ a & d \\ b & \end{matrix}\]