# Matrix multiplication - is this plausible?

1. Apr 8, 2014

say X = (AB) (B-1 C)

B-1 = B inverse (B B-1 = B-1 B = I)

then can i write X = AC?

just having a brain fart moment. i would appreciate a speedy response, cheers.

Last edited: Apr 8, 2014
2. Apr 8, 2014

### Simon Bridge

3. Apr 9, 2014

nah i just needed someone to verify that. thanks :)

4. Apr 9, 2014

No worries.

5. Apr 9, 2014

### HallsofIvy

Staff Emeritus
The "properties of matrix multiplication" that Simon Bridge referred to that are needed here are specifically the "associative law" and the definition of "inverse", that $BB^{-1}= I$

By the associative law, $(AB)(B^{-1}C)= A(BB^{-1})C$ and then $BB^{-1}= I$ gives $A(I)C= AC$.