1. Let's start by defining what a matrix is. A matrix is a rectangular array of numbers arranged in rows and columns. 2. A rectangular matrix is any matrix where the number of rows and columns are not necessarily equal. For example, a matrix with $m$ rows and $n$ columns, where $m \neq n$, is rectangular. 3. A square matrix is a special type of rectangular matrix where the number of rows equals the number of columns, i.e., $m = n$. 4. Important properties: - Rectangular matrices can have different numbers of rows and columns. - Square matrices have the same number of rows and columns. 5. Example: - Rectangular matrix: $$\begin{bmatrix}1 & 2 & 3 \\ 4 & 5 & 6\end{bmatrix}$$ (2 rows, 3 columns) - Square matrix: $$\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}$$ (2 rows, 2 columns) 6. Square matrices are important because they have special properties like determinants and eigenvalues, which rectangular matrices do not have. In summary, all square matrices are rectangular, but not all rectangular matrices are square.