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

1. anilorap

$A^{t}A=I$

2. Zarkon

for square matrices DET(AB)=Det(A)Det(B)

3. Zarkon

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

4. anilorap

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

5. Zarkon

$\det(A ^{t}) \det(A) =\det(I)=1$ $\det(A) \det(A) =1$ $\det(A)^2=1$ $\det(A)=\pm\sqrt{1}=\pm1$