Thread: 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

we can use (distribution law) and prove and disprove

for 1) see if you can find matrcies