# Equivalence Relation? Column-equivalence on the set of all $m\times n$ matrices.

How do I show that column equivalence on the set of all $m\times n$ matrices is an equivalence relation?

I know that to show it is an equivalence relation, I need to show that column equivalence is transitive, symmetric, and reflexive.

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Hint: the expression "column equivalence" does most of your work for you.

I know that to show it is an equivalence relation, I need to show that column equivalence is transitive, symmetric, and reflexive.

Just do exactly that: show that your column equivalence is transitive, symmetric, and reflexive on the set of all $m\times n$ matrices. To do this: