Matrix multiplication - is this plausible?

[catsarebad]

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.

 

[Simon Bridge]

You mean:

$X=(AB)(B^{-1}C) = AC$ ... you should be able to figure it out from the properties of matrix multiplication.
http://en.wikipedia.org/wiki/Matrix_multiplication

What you need to be true is: $A(BC)=(AB)C$ right?

 

[catsarebad]

You mean:

$X=(AB)(B^{-1}C) = AC$ ... you should be able to figure it out from the properties of matrix multiplication.

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

 

[Simon Bridge]

No worries.

 

[HallsofIvy]

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 $A(I)C= AC$.