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    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

    © BrainMass Inc. brainmass.com March 5, 2021, 12:03 am ad1c9bdddf

    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.