Chapter 6.2, Problem 64E

DISCUSS: Square Roots of Matrices A square root of a matrix B is a matrix A with the property that $A^2=B$ . (This is the same definition as for a square root of a number.) Find as many square roots as you can of each matrix:
$\left[\begin{array}{rr}\hfill 4& \hfill 0\\ \hfill 0& \hfill 9\end{array}\right]$ $\left[\begin{array}{rr}\hfill 1& \hfill 5\\ \hfill 0& \hfill 9\end{array}\right]$
[Hint: If $A=\left[\begin{array}{rr}\hfill a& \hfill b\\ \hfill c& \hfill d\end{array}\right]$ , write the equations that a, b, c, and d would have to satisfy if A is the square root of the given matrix.]