# prove that

• November 25th 2009, 01:41 AM
westdivo
prove that
Prove that if A is a non-singular matrix such that A^2 = A, then det(A) = 1?
• November 25th 2009, 01:45 AM
tonio
Quote:

Originally Posted by westdivo
Prove that if A is a non-singular matrix such that A^2 = A, then det(A) = 1?

Hint: for any two square matrices $A\,,\, B$ , $det(AB)=det A\cdot detB$

Tonio
• November 25th 2009, 01:47 AM
Defunkt
Since $A=A^2$, we know that $det(A^2)=det(A)$.

However, $det(A^2) = (det(A))^2$ for any matrix A. What does this, coupled with A being non-singular, give us?