- #1
WiFO215
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Homework Statement
Let R be the field of real numbers, and let D be a 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(I) != D ([0 1 1 0])
Prove that
a) D(0) = 0
b) D(A) = 0 if A2= 0
c) D(B) = -D(A) if B is obtained by interchanging the rows of A
d) D(A) = 0 if one row of A is 0
e) D(A) = 0 whenever A is singular
Homework Equations
The Attempt at a Solution
I can prove a) by assuming A=B=0. But that also leaves the case that D(0) = 1 which I don't know how to disprove. I'm clueless on the rest of them.