Matrix simplification

1. Oct 25, 2007

JFonseka

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

Simplify

A = HG(FHG)$$^{-1}$$FG

2. Relevant equations

None

3. The attempt at a solution

Well (FHG)^-1 is really just F^-1 H^-1 G^-1
Therefore A = HGG$$^{-1}$$H$$^{-1}$$F$$^{-1}$$FG
GG^-1 = I
FF-1 = I

Therefore A = HIH$$^{-1}$$(IG)

The book now simplifies to HH$$^{-1}$$G

I understand all the steps and the ending step, but I don't get how they got rid of the two I's

I X I = I (Identity Matrix), so where did it disappear to?

The final answer is: A = G

Thanks

2. Oct 25, 2007

JFonseka

Urgh, silly me, solved.

Identity matrix multiplied by another matrix just returns that matrix I forgot.

Silly problem. Sorry.

3. Oct 25, 2007

bala.l

Not really. (FHG)^-1 = (G^-1)*(H^-1)*(F^-1).