Spectral decomposition of some special matrices

Question

Let $A = \begin{pmatrix}a+b & a &0\\a & 2a & a\\0 & a & a+b \end{pmatrix}$ and $B = \begin{pmatrix}a+b & a &0 & 0\\a & 2a & a & 0\\0 & a & 2a & a\\0 & 0 & a & a+b \end{pmatrix}$, where $A$ and $B$ are invertible. Is it possible to find $A^{-1/2}$ and $B^{-1/2}$ such that $A^{-1} = A^{-1/2}A^{-1/2}$ and $B^{-1}=B^{-1/2}B^{-1/2}$?