1. a. Given A = compute the following,
i. A3
ii. A-3
iii. A2 - 2A + I
b. If a polynomial p(x) can be factored as a product of two lower degree polynomials p1(x) and p2(x) as
p(x) = p1(x)p2(x)
then it can be proved that p(A) = p1(A)p2(A) for an arbitrary square matrix A. Verify this statement for polynomials
p(x) = x2 - 9, p1(x) = x + 3, p2(x) = x - 3.
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