Problem, illustrate ways in which the algebra of matrices is not analogous to the algebra of real numbers.
(a) Suppose that A and B are the matrices of Example 5.
Show that (A + B)(A − B) ≠ A2 − B2.
(b) Suppose that A and B are square matrices with the properly that AB = BA. Show that (A + B)(A − B) = A2 − B2.
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