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Let A and B be invertible matrices such that 

 

A <2 , -1> = <1 , 2> and B <1 , 3> = <2 , -1>.

 

Calculate (AB)^{-1} <1 , 2>.

 Jul 6, 2019
 #1
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\((AB)^{-1}<1,2> =\\ B^{-1}A^{-1}<1,2>\)

 

\(A<2,-1> = <1,2>\\ <2,-1>=A^{-1}<1,2>\)

 

\(B<1,3>=<2,-1>\\ <1,3> = B^{-1}<2,-1>\)

 

\(B^{-1}A^{-1}<1,2> = \\ B^{-1}<2,-1> = \\ <1,3>\)

.
 Jul 6, 2019

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