# diagonalization problem

It's too easy question but I'm confused.

Let A matrix is \begin{pmatrix} 5 & 4\\ 4 & 5\\ \end{pmatrix}

Of course it can be diagonalized since it has distinct two eigenvalues.

The question is to find square roots, that is $R^2$=A.

I think there are two possible $R$, $A^\frac{1}{2}$ and $-A^\frac{1}{2}$

However the answer is four. What are the other two?

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Hint: $A$ has two distinct eigenvalues, and both of them have two square roots.