Find the inverse of a submatrix of a given matrix I have a $A$ matrix $4 \times 4$. By delete the first row and first column of $A$, we have a matrix $B$ with sizes $3 \times 3$. Assume that I have the result of invertible A that denote $A^{-1}$ before. I want to use the result to calculate the inverse of $B.$ Is it possible? Have any method to do it? Thanks 
Let consider a simple case that A is invertible then B also invertible. 

Maybe you can use one of the wikipedia pages:
http://en.wikipedia.org/wiki/Invertible_matrix#Blockwise_inversion
or 
http://en.wikipedia.org/wiki/Block_matrix_pseudoinverse
The pseudoinverse will have to be used in case B is not invertible. For instance the case in the other answer by 5xum.
