Simple Matrices proof using Mathematica help

[JJHK]

Simple Matrices proof using Mathematica help!

Homework Statement

Hey guys, I'm trying to prove that

(AB)^-1 = B^-1 A^-1
and also the one that looks the same but is with transpose of the matrices

making A and B arbitrary 3x3 matrices. I made

A = {{a_1,a_2,a_3}...}
B = {{b_1,b_2,b_3}...}

and I was able to prove the Transpose one by typing "Transpose[A B] == Transpose * Transpose[A] " and it spit out the word "True"

However, when I write "Inverse[A B] == Inverse Inverse[A] ", it does not spit out the word true, rather it spits back out the matrices expanded. Does anyone know how to tweak it so that it'll spit out either the words true or false? Thanks

Homework Equations

The Attempt at a Solution

 

[Simon Bridge]

making A and B arbitrary 3x3 matrices.

... and checking that the inverse exists?

when I write "Inverse[A B] == Inverse Inverse[A] ", it does not spit out the word true

check syntax - did you write the above or did you write:

Inverse[A B] == Inverse*Inverse[A]

(I can't remember if it matters)

I find that the inverse function does some rounding off, and the rounding is different if I do inverse[A*B] and when I do inverse[A]*inverse, so whenever I do Inverse[A*B] == Inverse*Inverse[A] it returns "false".