Inverse of a $4 \times 4$ triangular block matrix

Question

I need to find the form of the inverse matrix of this $4 \times 4$ triangular block matrix (if it exists): $$M= \begin{bmatrix} A&?&?&?\\ 0&B&0&?\\ 0&0&C&?\\ 0&0&0&D\\ \end{bmatrix} $$ Where $A, B, C, D$ are square matrices and with $'?'$ I've indicated some other entries of the square matrix which are unknown. Thanks for your help.

Answer 1

1. First invert D, then use it to by row operations solve ? in same column to 0.
2. Invert C, use it to solve away ? at top row.
3. Invert B, use it to solve away ? at top row.
4. Invert A

Done