Thread: orthogonal matrix

Prove that if Q is an orthogonal matrix, the det(Q)=(+-)1.

What ideas have you had so far?

Originally Posted by Ackbeet

What ideas have you had so far?

Actually I think I've got it. Using the two theorems (if allowed) of det(AB)=det(A)det(B) and detA=detA^t...without explict detail we will eventually end up (det(Q))^2=1 which will leave us with det(Q)= 1 or -1

Perfect. You don't need to add any more - I think you're done.