# Linear Algebra question

• February 4th 2011, 05:59 AM
maximus101
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
• February 4th 2011, 06:49 AM
we can use $A(B+C)=AB+AC$(distribution law) and $(B+C)A=BA+CA$ prove and disprove
for 1) see if you can find matrcies $A \text{ and }B\text{ such that }AB\neq BA$