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The matrices

\(A= \binom{1 \text{ }x}{y \text{ }1} \)

\(B = \binom{-1 \text{ } x}{y \text{ }-1}\)

are inverses

 

what is xy?

 Jul 6, 2019
 #1
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Because these are inverses   AB  = the identity matrix

 

[ 1  x  ]      *     [  - 1  x ]    =      [   1   0  ]

[  y  1 ]            [   y  - 1 ]           [    0   1 ]

 

So....by matrix multiplication, we have

 

[ - 1 +xy     x - x  ]  =    [  1   0   ]

[  -y + y      xy -1 ]        [   0   1  ]

 

Which implies that

 

xy - 1   =  1        add 1 to both sides

 

xy  =  2

 

cool cool cool

 Jul 6, 2019

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