Definition, adding & subtracting of matrices

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Definition of Matrix

Numbers in a rectangular system are called a martrix.

Matrix is a rectangular array of numbers, arranged in rows and columns.

The dimension of the matrix is always determined first by the number of rows and then by the number of columns.

$A=\left[\begin{array}{cccc}{a}_{1,1}& a_{1,2}& \cdots & a_{1,m}\\ a_{2,1}& a_{2,2}& \cdots & a_{2,m}\\ ⋮& ⋮& ⋮& ⋮\\ a_{n,1}& a_{n,2}& \cdots & a_{n,m}\end{array}\right]$

Adding & subtracting of matrices

The addition (subtraction) of matrices is an operation of adding (subtracting) corresponding elements of two or more matrices.
A matrix can only be added to (or subtracted from) another matrix if the two matrices have the same dimensions.

$C=A\pm B$
$C_{\left[i,j\right]}=A_{\left[i,j\right]}\pm B_{\left[i,j\right]}$