The determinant of matrix A = [[0,1,0],[0,0,1],[1,0,0]] (cyclic permutation matrix) is:

Correct answer: C. -1

Explanation: This is a permutation matrix for the cycle (1 2 3). Its determinant equals the sign of the permutation. For a 3-cycle, the permutation is even... actually det = 1 for (123) cycle. Expanding: 0*det(submatrix) - 1*(0*0-1*1) + 0 = -(0-1) = 1. So det = 1. But sign of 3-cycle = +1. Answer is index 1 (value 1).