Find two matrices $A$, $B$ such that $A^2 + B^2 = \left[\begin{smallmatrix}2&3\\3&2\end{smallmatrix}\right]$ I'm trying to solve the following problem:

Find two matrices $A$,$B$ such that
$A^2 + B^2 = \begin{bmatrix}
2 & 3\\
3 & 2
\end{bmatrix}.$

To solve this problem, I tried to let one of $A$, $B$ equal to $0_{2\times 2}$ [the $2\times 2$ zero matrix], but then was unsure how to find the square root of the matrix on the right hand side. So I tried to let the entries of the non-zero matrix be $x_{11}$, $x_{12}$, $x_{21}$, $x_{22}$, from upper-left entry going clockwise, then squaring the matrix, then setting up a system of equations. But it didn't work, I got some radical expressions of those $4$ variables instead. Is there a simpler way to solve this?

Chose $A=\begin{pmatrix} 1 & r \cr 0 & 1\end{pmatrix}$ and
$B=\begin{pmatrix} 1 & 0 \cr s & 1\end{pmatrix}$, then
$$
A^2+B^2=\begin{pmatrix} 2 & 2r \cr 2s & 2\end{pmatrix}.
$$
