2×2

2×2, read as "two by two" or "two by two," is a common mathematical notation with several related meanings.

In arithmetic, 2×2 denotes the product of 2 and 2, which equals 4.

It is also used to describe dimensions, such as a 2×2 grid or square, with two units in each direction and four cells.

In linear algebra, a 2×2 matrix is a square matrix with two rows and two columns, typically written as [[a, b], [c, d]]. The determinant is ad − bc, and the matrix is invertible when the determinant is nonzero, with inverse (1/(ad−bc))[[d, −b], [−c, a]].

A 2×2 matrix represents a linear transformation of the plane, including scaling, rotation, reflection, and shear, depending on its entries.

Common applications include solving systems of two linear equations, computer graphics, and representing small contingency tables in statistics.

Special cases include diagonal matrices [[a, 0], [0, d]] and the identity matrix [[1, 0], [0, 1]], which play fundamental roles in various calculations and transformations.