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
Follow Math Help Forum on Facebook and Google+
we can use $\displaystyle A(B+C)=AB+AC$(distribution law) and $\displaystyle (B+C)A=BA+CA$ prove and disprove
for 1) see if you can find matrcies $\displaystyle A \text{ and }B\text{ such that }AB\neq BA$
View Tag Cloud