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Order of a matrix

The order of a matrix is written as $m \times n$, where $m$ is the number of rows and $n$ is the number of columns. This is read as "$m$ by $n$". The order is also called the size of the matrix.

The matrix $\displaystyle\begin{pmatrix}0&1&0\\-1&0&0\end{pmatrix}$ is a $2\times 3$ matrix. It has $2$ rows, $3$ columns and $6$ entries.

We can find the number of elements by multiplying $m$ and $n$. Even though an $m \times n$ and an $n \times m$ matrix have the same number of elements, they do not have the same order.

A $2\times 3$ matrix and a $3\times 2$ matrix have different sizes though they have same number of elements (6).

The following matrices $$\begin{pmatrix}1&2&3\\4&5&6\end{pmatrix},\quad \begin{bmatrix}1&x\\1&y\\1&z \end{bmatrix},\quad \begin{pmatrix}1&1\\0&1\end{pmatrix},\quad \begin{bmatrix}1\\0\\-1\end{bmatrix}$$ are of order $2\times 3$, $3\times2$, $2\times 2$ and $3\times 1$.