Inverse of partitioned matrices A matrix of the form
$$A=\begin{bmatrix} A_{11} & A_{12}\\ 0 & A_{22} \end{bmatrix}$$
is said to be block upper triangular. Assume that $A_{11}$ is $p \times p$, $A_{22}$ is $q \times q$ and $A$ is invertible. Find a formula for $A^{-1}$.
Could anyone help on this?

Hint:
You may consider the matrix $$B = \begin{bmatrix} B_{11} & B_{12} \\ B_{21} & B_{22} \end{bmatrix},$$
such that:
$$\begin{bmatrix} A_{11} & A_{12}\\ 0 & A_{22} \end{bmatrix} \cdot \begin{bmatrix} B_{11} & B_{12} \\ B_{21} & B_{22} \end{bmatrix} = \begin{bmatrix} I_{p\times p} & 0 \\ 0 & I_{q\times q} \end{bmatrix},$$
where $B_{11}$ is a $p\times p$ matrix, $B_{12}$ is a $p\times q$ matrix, $B_{21}$ is a $q \times p$ matrix and $B_{22}$ is a $q \times q$ matrix.
