5. Answer the following (you need to show your work). (a) Give a 2 x 2 matrix A such that A2 = 0 but A = 0. (b) Give a 2 x 2 matrix B such that B2 = I but B±I (I is the identity matrix). (c) Write down a pair of 2 x 2 non-zero matrices A and B such that AB = 0 (0 is the 2 x 2 zero matrix) 6 (d) Given A = write down the elementary matrices E1, E2 and E3 such that 3 4 6 - [81]. A- [31] - E₂A = -3 E₁A = and E3 A=

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