# Find A

• April 6th 2010, 11:48 AM
wopashui
Find A
if AB =
[1 1]
[3 4] and $b^{-1}$=

[1 -1]
[1 2], find A

I know it's a simple question, i am just not sure if

$AB * B^{-1} = A$
• April 6th 2010, 01:26 PM
tonio
Quote:

Originally Posted by wopashui
if AB =
[1 1]
[3 4] and $b^{-1}$=

[1 -1]
[1 2], find A

I know it's a simple question, i am just not sure if

$AB * B^{-1} = A$

Yes.

Tonio
• April 7th 2010, 03:53 AM
HallsofIvy
By the "associative law", $(AB)B^{-1}= A(BB^{-1})$. By the definition of "multiplicative inverse", $BB^{-1}= I$ and by the definition of "multiplicative identity", $AI= A$.