(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.

Q: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

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Q: A^4-2A^3+A^2+4A+5l

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A: Explanation is given below..

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Q: , and c

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A: Let T:ℝ3→ℝ3 be a linear transformation defined by T(x,y,z)=x-y,y-z,z-x Therefore Ker T=x,y,z∈R3:…