- #1

donald17

- 6

- 0

## Homework Statement

Given the set of 3x3 matrices of the form: [1, a, b; 0, 1, c; 0, 0, 1], where a, b, and c are any real numbers show that the inverses of these matrices are of the same given form.

## Homework Equations

Using elementary row operations, transform [A:I] into [I:A

^{-1}].

Inverse of a 3x3 matrix

## The Attempt at a Solution

This is a subsection of a problem in which I am attempting to show that the set of these 3x3 matrices are a group under matrix multiplication. I was able to prove that it is well-defined, closed, an identity exists, and that associativity holds. For the inverse, it was simple to show that this set of 3x3 matrices is non-singular, but the trouble I'm running into is showing that the inverse is of the same given form so that closure still holds.

Thanks for any assistance.