The inverse of a matrix is a matrix such that is the identity matrix.

The trace of a matrix is the sum of the entries on the main diagonal (upper-left to lower-right).

The determinant is computed from all the entries of the matrix and is nonzero precisely when the matrix is nonsingular, that is, when the equation always has a unique solution.

The matrix rank is the number of linearly independent columns and is equal to three precisely when the matrix is nonsingular.

A number is an eigenvalue of if there is some nonzero vector such that ; the vector is called an eigenvector. In the result, the row of the eigenvector array is an eigenvector of unit length associated with the eigenvalue in the eigenvalue array.