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anilorap
 3 years ago
find the det(A), where A is a square matrix satisfying the property that A(transpose)A=
I
anilorap
 3 years ago
find the det(A), where A is a square matrix satisfying the property that A(transpose)A= I

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Zarkon
 3 years ago
Best ResponseYou've already chosen the best response.1for square matrices DET(AB)=Det(A)Det(B)

Zarkon
 3 years ago
Best ResponseYou've already chosen the best response.1I guess I should add that Det(I)=1 and Det(A)=Det(A^T)

anilorap
 3 years ago
Best ResponseYou've already chosen the best response.0so i have \[\det(A ^{t} A)=\det(I)\] \[\det(A ^{t}) \det(A) =\det(I)\]

Zarkon
 3 years ago
Best ResponseYou've already chosen the best response.1\[\det(A ^{t}) \det(A) =\det(I)=1\] \[\det(A) \det(A) =1\] \[\det(A)^2=1\] \[\det(A)=\pm\sqrt{1}=\pm1\]
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