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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we can use (distribution law) and prove and disprove
for 1) see if you can find matrcies
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