The top level matrix type in Axiom is Matrix, see (Matrix), which provides basic arithmetic and linear algebra functions. However, since the matrices can be of any size it is not true that any pair can be added or multiplied. Thus Matrix has little algebraic structure. Sometimes you want to use matrices as coefficients for polynomials or in other algebraic contexts. In this case, SquareMatrix should be used. The domain SquareMatrix(n,R) gives the ring of n by n square matrices over R. The usual arithmetic operations are available. Square matrices can be used where ring elements are required. For example, here is a matrix with matrix entries. Or you can construct a polynomial with square matrix coefficients. This value can be converted to a square matrix with polynomial coefficients. For more information on related topics see Modes and Matrix. Issue the system command to display the full list of operations defined by SquareMatrix.