Invertible Matrices within a Matrix Suppose A, B are invertible matrices of the same size. Show that 
$$M = \begin{bmatrix} 0& A\\ B& 0\end{bmatrix}$$ is invertible. 
I don't understand how I could show this. I have learned about linear combinations and spanning in my college class, but I don't know how that would help in this case. 

You can check directly that 
$$
M^{-1}=\begin{bmatrix} 0&B^{-1}\\ A^{-1}&0\end{bmatrix}. 
$$
