Complexity Explorer Santa Few Institute

Question 1: Recall that the determinant of a diagonal matrix is simply the product of the diagonal elements.  Here, that product is (1) (5) (9) = 45.

Question 2:  Recall that the determinant of the product of two matrices is equal to the product of the determinants.   Here we have det(BC) = det(B)det(C) = (-4)(-3) = 12.