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

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- Nov 25th 2009, 01:41 AMwestdivoprove that
Prove that if A is a non-singular matrix such that A^2 = A, then det(A) = 1?

- Nov 25th 2009, 01:45 AMtonio
- Nov 25th 2009, 01:47 AMDefunkt
Since $\displaystyle A=A^2$, we know that $\displaystyle det(A^2)=det(A)$.

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