Let A and B be (n x n)-matrices.
P1: If B is obtained from A by interchanging two rows, then det(B) = -det(A).
P2: If B is obtained from A by multiplying one row by k, then det(B) = k * det(A).
P3: If B is obtained from A by adding a multiple of one row to another row (leaving the first row unchanged), then det(B) = det(A).
P4: If A is an upper (or lower) triangular matrix, then det(A) = the product of the diagonal entries.
Use properties P1-P4 to find the determinant of the following complex matrix: