2x2 matrix inverse

1. Sep 24, 2008

hoffmann

I need to find the inverse of a 2x2 matrix of the form [a b ; c d]

I'm halfway there, but the algebra gets really messy. Could anyone help me out by doing the problem step by step? Thanks!

2. Sep 24, 2008

quasar987

I'm not going to do the problem for you, but I can give you a hint... you should be find that the inverse is of the form (1/ad-bc)M(a,b,c,d), where M(a,b,c,d) is a pretty simple 2x2 matrix.

3. Sep 24, 2008

hoffmann

thanks for the reply. i'm aware of the formula. in fact, i'm trying to derive the formula to prove to myself that i can do gauss jordan elimination. i just got stuck midway because the algebra gets pretty messy. here's where i am in the process:

[ a b ; c d | 1 0 ; 0 1 ] -->
[ a b ; (ac/c) (ad/c) | 1 0 ; 0 (a/c) ] -->
[ a b ; 0 ((ad/c)/c) -b | -1 (a/c) ] -->
...

i went a couple of steps ahead and i must not be doing something right. i'd appreciate if someone could lay it out for me on the site. thanks!

4. Sep 24, 2008

Defennder

I don't see how you got that. Starting from the matrix above that, multiply the 2nd row by -1 and add it to the first row. See how to continue from there?