UPSKILL MATH PLUS

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Additive Identity:
The null matrix or zero matrix which has all the elements as zero.

$$O = \begin{bmatrix} 0 & 0\\ 0 & 0 \end{bmatrix}$$
The zero matrices are the identity for matrix addition. When a zero matrix $$(O)$$ is added to any matrix, say $$A$$, the result is always the same matrix $$A$$.

Let $$A$$ be any matrix. Then, $$A+O =O +A = A$$.
Example:
Let's take the matrix $$A = \begin{bmatrix} 5 & 10\\ 4 & 8 \end{bmatrix}$$

So, $$A + O = \begin{bmatrix} 5 & 10\\ 4 & 8 \end{bmatrix} + \begin{bmatrix} 0 & 0\\ 0 & 0 \end{bmatrix} = \begin{bmatrix} 5 & 10\\ 4 & 8 \end{bmatrix}$$
Additive Inverse:
If $$A$$ be any given matrix then $$–A$$ is the additive inverse of $$A$$.
Example:
If $$A = \begin{bmatrix} 5 & -10 & 15\\ 6 & 8 & -7\\ -9 & 2 & 14 \end{bmatrix}$$ then $$- A = \begin{bmatrix} -5 & 10 & -15\\ -6 & -8 & 7\\ 9 & -2 & -14 \end{bmatrix}$$
Important!
When we add the two additive inverse matrices we get zero matrix

That is $$A+(−A) = (−A)+A =O$$