Skill: Determine the dimensions of a matrix

To find a matrix’s dimensions, count its rows first (horizontal lines of entries), then its columns (vertical lines of entries). Write the result as rows $\times$ columns.

For example, consider

$$A=\begin{bmatrix} 2 & -1 & 4\\ 0 & 3 & 5 \end{bmatrix}.$$

1. Count the horizontal rows: there are $2$.
2. Count the vertical columns: there are $3$.
3. Write rows $\times$ columns: $A$ is a $2\times 3$ matrix.

The dimensions describe the matrix’s rectangular shape, not the values of its entries. Since $2\ne 3$, this matrix is not square.