A matrix is an arrangement of ‘cells’ in rows and columns. A spreadsheet is a simple example of a matrix. Each cell is described by its position in a column, normally denoted by an alphabetical letter, and in a row, normally denoted by a number. So ‘cell B6’ on your spreadsheet is the one which occupies column B and row 6. The size of a matrix is described by the number of rows and the number of columns (in that order).
A ‘two-by-two’ matrix has two rows and two columns. A ‘three-by-two’ matrix has three rows and two columns.