Dimensions of a Matrix

The dimensions of a matrix are the number of rows by the number of columns.  If a matrix has a rows and b columns, it is an a × b matrix.  For example, the first matrix shown below is a 2 × 2 matrix; the second one is a 1 × 4 matrix; and the third one is a 3 × 3 matrix.

When you add and subtract matrices, their dimensions must be the same; when you multiply them, their dimensions must be compatible.