Question

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

Answer 1

\[A^{t}A=I\]

Answer 2

for square matrices

DET(AB)=Det(A)Det(B)

Answer 3

I guess I should add that Det(I)=1 and Det(A)=Det(A^T)

Answer 4

so i have
\[\det(A ^{t} A)=\det(I)\]
\[\det(A ^{t}) \det(A) =\det(I)\]

Answer 5

\[\det(A ^{t}) \det(A) =\det(I)=1\]

\[\det(A) \det(A) =1\]

\[\det(A)^2=1\]

\[\det(A)=\pm\sqrt{1}=\pm1\]