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Consider a square Block matrix

M_block = \begin{bmatrix} A &B \\ C& D \end{bmatrix}

where, A, B, C and D are sub-matrices.

I know computational complexity of the above block matrix by general inverse technique would be $O(n^3)$ if size of the above matrix is of $n\times n$.

Two queries:

First: What will be the computational and space complexity if calculate the inverse by using block-inverse matrix method?

Second: What will be the computational and space complexity if calculate the inverse by using block-inverse matrix method and inverse of $A$ is given?

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