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?