Ch. 1, Sect. 4, Problem 10 (b)
     
If p1(x) = x2 - 9, p2(x) = x - 3, and p3(x) = x + 3, then whatever the square matrix A we have

p1(A) = AA - 9I,
p2(A) = A - 3I, and
p3(A) = A + 3I,
so that

    p2(A) p3(A) = (A - 3I)(A + 3I) =
= AA - 3(IA) + 3(AI) - 9(II) =
= AA - 3A + 3A - 9I =
= AA - 9I = p1(A)

(here I stands for the (square) identity matrix the same size and shape as the original square matrix A).

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