Blockwise inversion for calculate the inverse of the block matrix?

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I have the matrix:

$ M^{-1} = \begin{pmatrix}X & Y\\\ Z & W\end{pmatrix}$

But I do not know the matrix:

$ M = \begin{pmatrix}A & B\\\ C & D\end{pmatrix}$

Is possible calculate $ A^{-1} $, no need to invert the matrix $M^{-1}$ (Using Blockwise inversion, it is easy calculate $A^{-1} B = Y U^{-1}$ and $C A^{-1} = Z U^{-1}$, but just $ A^{-1} $, I could not calculate)??