6. Prove that (AC) = C" A" 7. Suppose that A is an invertible matrix and AB = I Then (a) Show that BA = I. and (b) And the matrix B such that AB = BA = I¸ is unique. 1 -2 1 8. Given A = -3 7 - 6 (a)...

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Extracted text: 6. Prove that (AC) = C" A" 7. Suppose that A is an invertible matrix and AB = I Then (a) Show that BA = I. and (b) And the matrix B such that AB = BA = I¸ is unique. 1 -2 1 8. Given A = -3 7 - 6 (a) find A (b) Use part (a) to solve AX = b 2 -3 where b = -2 Eigen-values and Eigen-vectors and Diagonalization 9. for the given matrix below fiind (a) The characteristic equation; (b) The eigenvalues; (c) bases for the eigenspaces; (d) is the matrix diagonlizable? Expain. 0 -1 3 1 2