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Proof: (related to "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 $M_{m\times n}(F)$.

Ad $(1)$

Ad $(2)$

Ad $(3)$

Ad $(4)$

q.e.d

| | | | created: 2020-11-29 11:35:18 | modified: 2020-11-29 12:00:18 | by: bookofproofs

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