Question: (a) If the matrix show that A 2 = I and derive the elements of a square matrix B which satisfies A 2 = I

(a) If the matrix

[100] A = 1 -1 0 1 1-2 -2

show that A2 = I and derive the elements of a square matrix B which satisfies

14 3 2 21 BA = 0 -1 0 0

A2 = I means that the inverse of A is A itself.

(b) Find suitable values for k in order that the following system of linear simultaneous equations is consistent:

6x + (k - 6)y= 3 2x + y = 5 (2k + 1)x + 6y = 1

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