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Math Help - Linear Algebra question

  1. #1
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    Linear Algebra question

    are these identities satisfied by all n by n matrices A and B? I is the n by n identity matrix? Proof if yes or counterexample if not required.

    1) (A-B)(A+B)= (A^2) - (B^2)
    2) (A-I)((A^2) + A + I)= (A^3)-I
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  2. #2
    Senior Member BAdhi's Avatar
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    we can use A(B+C)=AB+AC(distribution law) and (B+C)A=BA+CA prove and disprove
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  3. #3
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    for 1) see if you can find matrcies A \text{ and }B\text{ such that }AB\neq BA
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