Answer to Question #135361 in Abstract Algebra for Sohan kumar

Question #135361
Give a non zero function from M3 (Z) to Z.
1
Expert's answer
2020-09-29T15:16:51-0400

Define the function f:M3(Z)Zf: M_3(\mathbb Z)\to \mathbb Z in the following way:


f([aij]3×3)=a11+a22+a33f([a_{ij}]_{3\times 3})=a_{11}+a_{22}+a_{33}, where aijZ.a_{ij}\in\mathbb Z.


This function is non-zero because f(E)=1+1+1=30f(E)=1+1+1=3\ne 0 for the identity matrix EM3(Z)E\in M_3(\mathbb Z).


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