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: M_3(\\mathbb Z)\\to \\mathbb Z" in the following way:


"f([a_{ij}]_{3\\times 3})=a_{11}+a_{22}+a_{33}", where "a_{ij}\\in\\mathbb Z."


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


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