Prove that if A is a non-singular matrix such that A^2 = A, then det(A) = 1?
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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 $\displaystyle A\,,\, B$ , $\displaystyle det(AB)=det A\cdot detB$ Tonio
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?
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