MATRICES AND DETERMINANTS
Higher Concepts of Mathematics
Multiplication of a Matrix by a Matrix
To multiply two matrices, the first matrix must have the same number of rows (m) as the second
matrix has columns (n). In other words, m of the first matrix must equal n of the second matrix.
For example, a 2 x 1 matrix can be multiplied by a 1 x 2 matrix,
or a 2 x 2 matrix can be multiplied by a 2 x 2. If an m x n matrix is multiplied by an n x p
matrix, then the resulting matrix is an m x p matrix. For example, if a 2 x 1 and a 1 x 2 are
multiplied, the result will be a 2 x 2. If a 2 x 2 and a 2 x 2 are multiplied, the result will be a
2 x 2.
To multiply two matrices, the following pattern is used:
aw by ax bz
cw dy cx dz
In general terms, a matrix C which is a product of two matrices, A and B, will have elements
given by the following.
cij = ai1b1j + aj2b2j + + + . . . + ainbnj
i = ith row
j = jth column
Multiply the matrices A x B.