9×9

9×9, read as "nine by nine" or "nine times nine," denotes a two-dimensional extent with nine units along each of two perpendicular directions. In arithmetic, 9×9 equals 81, so a 9×9 rectangle has an area of 81 square units when each unit is taken as a square of side length one.

9×9 matrices are square matrices with nine rows and nine columns. They feature in linear algebra and numerical methods, where properties such as determinant and invertibility depend on the entries. The term is also used to describe grids or boards that have nine units per side.

In games and puzzles, the most common reference is the Sudoku grid: a 9×9 grid divided into nine 3×3 subgrids. Standard Sudoku puzzles require filling digits 1 through 9 so that each row, column, and subgrid contains every digit exactly once.

Outside mathematics, 9×9 grids appear in applications such as 9×9 LED dot matrices for displays, cross-stitch patterns, and pixel-based art. The 81 cells of a 9×9 grid make it a compact structure for various combinatorial and visualization tasks.