15) Using the properties of determinants or otherwise, show that 1 a² + a²³ 1 a+a²³=0. 1 a a² a³ a+a²

Fill in the blanks with appropriate numbers to calculate the determinant. (a) 9 - • 4 = %3D 1 -1 -3 (b) = ? v1 : O: -3) = 3 -4 1 • 0 - • 2) 3 . -3) • 1 - 2

1. (10 pts.) Compute the determinant of 2 0 0 0 -3 2 2 1 4 0 -3 -2 3 3 0 -1 0 0 6 0 1 -1 0

Let 1 2 -1 0 2 1 A = 1 and B 1 1 1 Compute the determinants of AB and BA.