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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- Feb 4th 2011, 05:59 AMmaximus101Linear 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 - Feb 4th 2011, 06:49 AMBAdhi
we can use $\displaystyle A(B+C)=AB+AC$(distribution law) and $\displaystyle (B+C)A=BA+CA$ prove and disprove

- Feb 4th 2011, 08:26 AMfizzle45
for 1) see if you can find matrcies $\displaystyle A \text{ and }B\text{ such that }AB\neq BA$