# Math Help - Homework help! Matrix determinant question?

1. ## Homework help! Matrix determinant question?

What is wrong with the proof that projection matrices have det (P) = 1?

P = A(AtA)^-1At

so

|P| = |A| (1/ (|At| |A|)) |At| = 1

I understand that that det (AB) = |A| |B|, so what's wrong with this proof?

2. If you are given that $P = A(A^{T}A)^{-1}A^T$, since A is not necessarily square so that det(A) is not necessarily defined, a safe tact is to show that $P^2=P$.

3. Originally Posted by Unco
a safe tact is to show that $P^2=P$.
What is the only number that fits the equation?
$x=x^n$