I have a matrix $ \begin{bmatrix} 9 & 6 \\ 6 & 9 \\ \end{bmatrix} $
I am tasked with finding two different symmetric positive definite matrices B such that $A = B^2$
I found one root using $B = U \Lambda^{1/2} U^{-1}$, with normalized eigenvectors $U = \begin{bmatrix} 1/\sqrt(2) & 1/\sqrt(2) \\ -1/\sqrt(2) & 1/\sqrt(2) \\ \end{bmatrix}$ and eigenvalues $\Lambda= \begin{bmatrix} 3 & 0 \\ 0 & 15 \\ \end{bmatrix}$, but I am confused about how to find a 2nd root. Wikipedia states: A positive-definite matrix has precisely one positive-definite square root.
It seems as though I am being asked to find another root that cannot exist. If I were to brute force the equations from $$\begin{bmatrix} a & b \\ c & d \\ \end{bmatrix}*\begin{bmatrix} a & b \\ c & d \\ \end{bmatrix} = \begin{bmatrix} 9 & 6 \\ 6 & 9 \\ \end{bmatrix}$$ would I be able to find another positive definite root?