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Math Help - (Help) square matrices

  1. #1
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    (Help) square matrices

    Suppose that A and B are square matrices of order n. For each statement:
    (a) (A-B)^2 = A^2 - 2AB + B^2
    (b) (A+B)(A-B) = (A-B)(A+B)
    (c) (A+B)^2 - (A-B)^2 = 2(AB +BA)

    either prove the equation is always true or give an example to show that it is false. If the equation is false, can you fund an condition which would make it generally true?
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  2. #2
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    Quote Originally Posted by 450081592 View Post
    Suppose that A and B are square matrices of order n. For each statement:
    (a) (A-B)^2 = A^2 - 2AB + B^2
    (b) (A+B)(A-B) = (A-B)(A+B)
    (c) (A+B)^2 - (A-B)^2 = 2(AB +BA)

    either prove the equation is always true or give an example to show that it is false. If the equation is false, can you fund an condition which would make it generally true?

    Hints: Only (3) is true in general (open up parentheses and see), (1) and (2) are false unless AB = BA. Now you look for examples!

    Tonio
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