# How do you find P^2 given P=((3, 1), (1, 3))?

Jun 25, 2016

${P}^{2} = \left(\begin{matrix}10 & 6 \\ 6 & 10\end{matrix}\right)$

#### Explanation:

${P}^{2}$ means multiply the matrix by itself, following the usual method for multiplying matrices.

${P}^{2} = \left(\begin{matrix}3 & 1 \\ 1 & 3\end{matrix}\right) \left(\begin{matrix}3 & 1 \\ 1 & 3\end{matrix}\right)$

$= \left(\begin{matrix}3 \times 3 + 1 \times 1 & 3 \times 1 + 1 \times 3 \\ 1 \times 3 + 3 \times 1 & 1 \times 1 + 3 \times 3\end{matrix}\right)$

$= \left(\begin{matrix}10 & 6 \\ 6 & 10\end{matrix}\right)$