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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Originally Posted by wopashui 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 $ Yes. Tonio
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", $\displaystyle AI= A$.