3x3

3x3, read as three by three or three times three, is a shorthand used to describe a square array with three rows and three columns. The term appears across mathematics, games, sports, and design to indicate that a structure has nine elements arranged in a grid of equal dimensions.

In mathematics, a 3x3 matrix is a matrix with three rows and three columns. Such matrices form the basis of linear transformations in three-dimensional space. The determinant and inverse exist unless the matrix is singular. The 3x3 identity matrix serves as the neutral element under matrix multiplication. Beyond matrices, 3x3 grids are used in coordinate representations, numerical methods, and tensor-related contexts.

In games and puzzles, a 3x3 grid is central to tic-tac-toe, where players alternate placing marks with the aim of forming a straight line. The game is solved; optimal play typically results in a draw.

In sport, the term 3x3 refers to a basketball variant played with three players per side on a half court. It is governed by FIBA rules and has its own competition circuit and Olympic status since 2020. The game emphasizes speed and spacing, with a scoring system that differs from standard 5-on-5 play (points awarded based on shot location).

In computing and design, 3x3 appears in image processing as a convolution kernel or neighborhood, and in user interface layouts where a 3-by-3 grid of icons or thumbnails is common.