(a) [3 marks] Let A be an invertible matrix, use the definition of the inverse matrix to prove that AT is invertible, and (AT)¯ = (A-1)". 1 -2 1 (b) [6 marks] Find the inverse of the matrix A = 4 -7 3 -2 6 -3 (c) [4 marks] Let A be an nxn matrix such that A³ = 0. Show that (I- A)(I+A+A²) = I, and (I – A)-1 = I + A + A².

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A: 1.a A=123-111201A=11-0-2-1-2+30-2     =1+6-6     =1determinant of A is not zero, therefore inverse…

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A:

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A:

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A:

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