Solving a matrix equation of four unknowns Find all matrices $A$ that satisfy $$A^2 - 4 A + 4I = \begin{pmatrix} 4 & 3 \\\ 5 & 6 \end{pmatrix}.$$ I've tried solving this but I can only get a single equation constraining $b$ and $c$, i.e. $b/c=3/5$. I find it difficult to solve for the rest. Can anybody give me a hint? Thanks

_Hints:_

1. $A^2 - 4A + 4I = (A - 2I)^2$
2. The matrix on the right hand side is positive definite.