(related to Proposition: Abelian Group of Matrices Under Addition)

The proof is very easy but long since it only requires the verification of the rules for the matrices $M_{m\times n}(F)$ over a field $F$ component by component. We will use two different symbols to distinguish between the addition of the components "$+$" in the field $F$ and the addition of matrices $\oplus$ in $M_{m\times n}(F)$.

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