I finished this problem but I'm not sure if what I did was mathematically legal. This is a homework problem but I'm hesitant to turn it in the way it is since it's worth a lot of points. If someone can confirm what I did is correct or incorrect, I'd really appreciate it, thanks! 1. The problem statement, all variables and given/known data Prove that if a matrix A is idempotent (A^2 = A), then the determinant of A is 0 (det(A) = 0). 2. Relevant equations None 3. The attempt at a solution 1) A^2 = A 2) AA = A 3) AA - A = A - A <- Here, I subtracted A from both sides 4) AA - A = 0 <- property of the Zero matrix (A+(-A) = 0) 5) A(I-A) = 0 <- I factored out A here, not sure if this is legal or not in matrices. A(I-A) = 0 implies that either I-A = 0 or A = 0; det(0) = 0, therefore, det(A) = 0.