# Answer to Question #4997 in Abstract Algebra for Annemarie

Question #4997

Consider the function f : Z4 → Z12 defined by f(x) = 3x. Show that f(x) does

NOT preserve multiplication.

NOT preserve multiplication.

Expert's answer

f:Z

We will show that this function does not preserve multiplication. we can consider x,y from Z

let x=1, y=3 so we have:

f(1*3)=f(3)=9 (modulo 12)

f(1)*f(3)=3*9=27=3( modulo 12)

But 9 is not equal to 3 in Z

_{4}--> Z_{12}, f(x)=3xWe will show that this function does not preserve multiplication. we can consider x,y from Z

_{4}such thatlet x=1, y=3 so we have:

f(1*3)=f(3)=9 (modulo 12)

f(1)*f(3)=3*9=27=3( modulo 12)

But 9 is not equal to 3 in Z

_{12}. So f does not preserve multiplication.Need a fast expert's response?

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