A matrix is a rectangular array of numbers or number-like elements:

In the example on the left, 1 1 and 2 0 are its rows; 1 2 and 1 0, its columns. In the example on the right there are three rows and two columns, making it a 3 x 2 matrix. When subscripted variables are used to represent the elements, the first subscript names the row,; the second, the column: a _{row, column}. For example, a ₂₁ is in the second row and first column, but a₁₂ is in the first row, second column. Except when there is danger of confusion, the subscripts need not be separated by a comma. Some authors enclose a matrix in brackets: other authors use parentheses, as above.

Matrices can also be represented with single letters A, I, or with a single subscripted variable (a_ij = b_ij) if and only if a_ij = b_ij for all i, j which says symbolically...