Thread: How would you show matrices of this form have an inverse of the same form?

Given this form of matrices: [1, a, b; 0, 1, c; 0, 0, 1], where a, b, and c are any real numbers.

How would you go about proving that matrices of this form have inverses of the same form? It's simple to prove that matrices of this form have an inverse in general, but I'm not sure where to go in proving that each inverse will be of the same form. Thanks for any help.

Have you tried taking the matrix $\displaystyle [A:I]$ and using ERO's to get to the matrix $\displaystyle [I:A^{-1}]?$ That might work.

Solved. Thanks.

You're welcome. Have a good one!