Find Inverse of 2x2 Matrix: Step-by-Step Guide

[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!

 

[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.

 

[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!

 

[Defennder]

[ 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 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?

EDIT: Please don't double-post threads. You've already posted this here:
https://www.physicsforums.com/showthread.php?t=258994