Definition of a matrix
A matrix is a set of numbers arranged in rows and columns to form a rectangular or a square array.
What is order of a matrix?
Order of a matrix can be determined by counting the number of rows followed by the number of columns of the matrix. Matrix with \(m\) rows and \(n\) columns has the order \(m\times n\) and is read as “matrix \(m\) by \(n\). For example,
For example:
\(\begin{aligned}\begin{bmatrix} 2&3&7\\ 5&4&9 \end{bmatrix}\end{aligned}\)
This matrix has \(2\) rows and \(3\) columns. Therefore, it is a matrix with order \(2\times 3\) and can be read as “matrix \(2\) by \(3\)”.
Example 1
Given that matrix \(K=\begin{aligned}\begin{bmatrix} -2&3\\ 0&4\\1&9\end{bmatrix}\end{aligned}\), determine
a) the order of the matrix, 
b) the elements \(d_{11}\)\(d_{21}\) and \(d_{32}\).

a)Since D has \(3\) rows and \(2\) columns,

\(\therefore \) D has order \(3\times 2\)


\(\begin{aligned} b)\hspace{1mm} &d_{11}=-2\end{aligned}\)

\(\because\) \(d_{11}\) is the element at the first row and first column.


\(\because\) \(d_{21}\)  is the element at the second row and first column.

\(\begin{aligned} d_{32}=9\end{aligned}\)

\(\because\) \(d_{32}\) is the element at the third row and second column.

Equal matrices
Matrixces A and B are equal, A = B if the order of both the matrices are the same and the corresponding elements are equal. 

\(\begin{aligned} \begin{bmatrix} a&b\\ c&d \end{bmatrix} = \begin{bmatrix} e&f\\ g&h \end{bmatrix} \end{aligned}\)

\(\begin{aligned} \implies a&=e, \\b&=f,\\c&=g,\\d&=h \end{aligned}\)