# Show that matrices of defined form have inverse of the same same defined form

1. Sep 22, 2010

### donald17

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Using elementary row operations, transform [A:I] into [I:A-1].
Inverse of a 3x3 matrix

3. 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.

2. Sep 22, 2010

### Staff: Mentor

What trouble are you having? Finding the inverse is straightforward, and yields the inverse in just a few steps. The inverse has the same form.

3. Sep 22, 2010

### donald17

Actually I just solved it. Thanks.