I know that to check for the equivalence relation, we would have to check for reflexivity, symmetry, and transitivity, but I'm very unfamiliar on how to do that with matrices.
Any help or a fully worked out solution would be appreciated!
2026-03-30 15:11:51.1774883511
Equivalence Relation on $2 \times 2$ Matrix
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Row equivalence means that there is a product $E$ of elementary matrices such that $B=EA$. It is reflexive because you can take $E=I$ to get $A=IA$. It is symmetric because row operations are reversible, and so $B=EA$ if and only if $A=E^{-1}B$. And it is transitive because the product of products of elementary matrices is a product of elementary matrices: if $B=EA$, $C=FB$, then $C=(FE)A$.