Properties of Matrix Exponential

Theorem
In the following:
 * $\mathbf A$ and $\mathbf B$ are constant square matrices of order $m$ for some $m \in \Z_{\ge 1}$
 * $\mathbf P$ is a non-singular square matrix of order $m$
 * $t, s \in \R$ are arbitrary real numbers.

The matrix exponential $e^{\mathbf A t}$ has the following properties: