Matrix Simplification: A = HG(FHG)^{-1}FG | Step-by-Step Solution

[JFonseka]

Homework Statement

Simplify

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

Homework Equations

None

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

 

[JFonseka]

Urgh, silly me, solved.

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

Silly problem. Sorry.

 

[bala.l]

Well (FHG)^-1 is really just F^-1 H^-1 G^-1

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