1. (a) [3 marks] Find a 3 x 3 matrix A such that :1: 112,: A y = 321; 2: 13322 for all r,y,z E R. 12 11 [c] [3 marks] Find all 2 x 3 matrices B such that (h) [4 marks] Let A = ( ). Find all 2 x 2 matrices B such that AB = BA. 2 U B 1 1 =(_32 El). 1 U 2. Let 1 {1+2 0 A: 1 1 3111 1 a n for some real number a. (a) [7 marks] For what values of a is A invertible? For these values of a, express the inverse of A as a product of elementaryr matrices, 1511 = Ek - - - EgEl- Leave your answer in terms of a if necessary. Hint: You do not need to nd A'1 explicitly. [b] [3 marks] Find the determinant of A. Show your workings clearly. Leave your answer in terms of a. For what value of a is the determinant nonzeroJ det [A] 35 0