Linear Algebra problem with proof
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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
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Solution Summary
This solution helps with a linear algebra problem with proof.
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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)= ...
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