1) An n × m determinant is the same as an n × m matrix.
2) Determinants are useful in solving a set of simultaneous equations.
3) A determinant has a single numerical value.
4) An n × m matrix, when added to an m × n matrix (n ? m), yields an n × n matrix.
5) The matrix multiplication (AB), where A and B are any matrix, is equal to the matrix multiplication (BA).
6) An n × m matrix, when multiplied by an m × n matrix, yields an n × n matrix.
7) An n × m matrix, when multiplied by an m × p matrix, yields an n × p matrix.
8) A cofactor of a matrix is the set of numbers that remains after a given row and column have been removed from a matrix.
9) An adjoint is the transpose of the matrix of cofactors.
10) A-1A = A A-1 = I
11) An n × m matrix multiplied by a p × m matrix yields an n × p matrix.
12) The subtraction of an n × m matrix from an n × m matrix yields an n × m matrix.
13) We can develop an n × m matrix by the addition of an n × m matrix and an n × p matrix, where p < n. 14) We can develop an n × m matrix by adding an n × p matrix and an n × r matrix where p + r = m. 15) We can always perform the matrix multiplication AA.
