Addition of Two Matrices

==2024-11-20

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Theory

Set for Addition Mathematical Operations

Let, $M_{m\times n}(\mathbb{F})$ be the set of all $m\times n$ matrices over a field $\mathbb{F}(\mathbb{R}/\mathbb{C})$ with addition operator.

So, $(M_{m\times n}(\mathbb{F}),+)$ is a Mathematical Group.

Properties of Matrix Addition

Then for all $A,B,C\in M_{m\times n}(\mathbb{F})$, we have the following properties,

1. $A+B=B+A$ → Commutative
2. $(A+B)+C=A+(B+C)$ → Associative
3. $A+\bar{0}=\bar{0}+A=A$ → Additive identity ($\bar{0}$)
4. $A+(-A)=\bar{0}=(-A)+A$ → Additive Inverse (-A)

On the basis of above Mathematical Properties, the Mathematical Group $(M_{m\times n}(\mathbb{F}),+)$ is an Abelian Group.

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Examples

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Implementation

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Q&A

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