Let $A \in \mathbb{R}^{2 \times 2}$ be a D4571: Real matrix.
Then
| (1) | \begin{equation} A^T A = \begin{pmatrix} A^2_{1 1} + A^2_{2 1} & A_{1 1} A_{1 2} + A_{2 1} A_{2 2} \\ A_{1 2} A_{1 1} + A_{2 2} A_{2 1} & A^2_{1 2} + A^2_{2 2} \end{pmatrix} \end{equation} |
| (2) | \begin{equation} A A^T = \begin{pmatrix} A^2_{1 1} + A^2_{2 1} & A_{1 2} A_{1 1} + A_{2 2} A_{2 1} \\ A_{1 1} A_{1 2} + A_{2 1} A_{2 2} & A^2_{1 2} + A^2_{2 2} \end{pmatrix} \end{equation} |