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If A and B are 4x4 matrices, det(A) = -4, det(B) = 3, then (h) det((8A)^-1) = ????

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luessssss | Student | eNoter

Posted April 28, 2013 at 1:24 AM via web

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If A and B are 4x4 matrices, det(A) = -4, det(B) = 3, then

(h) det((8A)^-1) = ????

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted April 28, 2013 at 5:53 AM (Answer #1)

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We will use the following two properties of determinants:

1) `det(cA)=c^ndet(A),` `c in RR` when `A` is `nxxn` matrix

2) `det(A^(-1))=1/(det(A))`

Hence we have

`det((8A)^(-1))=1/(det(8A))=1/(8^4det(A))=1/(2^12cdot(-4))=-1/2^14`

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