In mathematics, a matrix
(plural matrices, or less commonly matrixes) is a rectangular array of numbers, as shown at the right. One use of
matrices is to keep track of the coefficients in a system of linear equations. Matrices can also represent linear
transformations, which are higher-dimensional analogs of linear functions of the form f(x) = cx, where c is a
constant. They can be added and subtracted entry-wise, and multiplied according to a rule corresponding to
composition of linear transformations. These operations satisfy the usual identities, except that matrix
multiplication is not commutative: the identity AB=BA can fail. For a square matrix, the determinant and inverse
matrix (when it exists) govern the behavior of solutions to the corresponding system of linear equations, and
eigenvalues and eigenvectors provide insight into the geometry of the associated linear transformation.

- Wikipedia