1) An n à m determinant is the same as an
n à m matrix.
2) Determinants are useful in solving a
set of simultaneous equations.
3) A determinant has a single numerical
value.
4) An n à m matrix, when added to an m à n
matrix (n ≠ m), yields an n à n matrix.
5) The matrix multiplication (AB),
where A and B are any matrix, is equal to the matrix
multiplication (BA).
6) An n à m matrix, when multiplied by an
m à n matrix, yields an n à n matrix.
7) An n à m matrix, when multiplied by an
m à p matrix, yields an n à 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 à m matrix multiplied by a p à m
matrix yields an n à p matrix.
12) The subtraction of an n à m matrix
from an n à m matrix yields an n à m matrix.
13) We can develop an n à m matrix by the
addition of an n à m matrix and an n à p matrix, where p < n.
14) We can develop an n à m matrix by
adding an n à p matrix and an n à r matrix where p + r = m.
15) We can always perform the matrix
multiplication AA.
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