Let $A_1 \in \mathbb{R}^{N_1 \times N_2}, A_2 \in \mathbb{R}^{N_2 \times N_3}, \ldots, A_M \in \mathbb{R}^{N_M \times N_{M + 1}}$ each be a D4571: Real matrix.

Then \begin{equation} \left( A_1 A_2 A_3 \cdots A_{M - 2} A_{M - 1} A_M \right)^T = A^T_M A^T_{M - 1} A^T_{M - 2} \cdots A^T_3 A^T_2 A^T_1 \end{equation}

Let $A_1 \in \mathbb{R}^{N_1 \times N_2}, A_2 \in \mathbb{R}^{N_2 \times N_3}, \ldots, A_M \in \mathbb{R}^{N_M \times N_{M + 1}}$ each be a D4571: Real matrix.

Then \begin{equation} \left( \prod_{m = 1}^M A_m \right) = \prod_{m = 1}^M A^T_{M + 1 - m} \end{equation}