if AB =

[1 1]

[3 4] and $\displaystyle b^{-1} $=

[1 -1]

[1 2], find A

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

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

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- Apr 6th 2010, 11:48 AMwopashuiFind A
if AB =

[1 1]

[3 4] and $\displaystyle b^{-1} $=

[1 -1]

[1 2], find A

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

$\displaystyle AB * B^{-1} = A $ - Apr 6th 2010, 01:26 PMtonio
- Apr 7th 2010, 03:53 AMHallsofIvy
By the "associative law", $\displaystyle (AB)B^{-1}= A(BB^{-1})$. By the definition of "multiplicative inverse", $\displaystyle BB^{-1}= I$ and by the definition of "multiplicative identity", $\displaystyle AI= A$.