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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 $$3\times 1$$.