# 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

https://brainmass.com/math/linear-algebra/linear-algebra-problem-proof-478000

#### Solution Preview

Consider the matrix [0,1;1,0]. This is equal to itself times the identity, so [0,1;1,0] = [0,1;1,0][1,0;0,1] = [0,1;1,0]I.

Then, D([0,1;1,0]) = D([0,1;1,0]I)= ...

#### Solution Summary

This solution helps with a linear algebra problem with proof.

$2.49