Question:
Linear Algebra problem with proof
Let R be the field of real numbers, and let D be the function on 2x2 matrices over R with values in R, such that D(AB)=D(A)D(B) for all A, B. Suppose that D([0,1;1,0])=/D([1,0;0,1]).
Prove that:
1. D([0,0;0,0])=0
2. D(A) = 0 if A^2=0