This definition says that C(i,j) is the inner
product of the ith row of A with
the jth column of B. You can
write this definition using the MATLAB^{®} colon operator as

C(i,j) = A(i,:)*B(:,j)

For
nonscalar A and B, the number
of columns of A must equal the number of rows of B.
Matrix multiplication is not universally commutative
for nonscalar inputs. That is, A*B is typically
not equal to B*A. If at least one input is scalar,
then A*B is equivalent to A.*B and
is commutative.

C = mtimes(A,B) is
an alternative way to execute A*B, but is rarely
used. It enables operator overloading for classes.

Create a 1-by-4 row vector, A, and
a 4-by-1 column vector, B.

A = [1 1 0 0];
B = [1; 2; 3; 4];

Multiply A times B.

C = A*B

C =
3

The result is a 1-by-1 scalar, also called the dot
product or inner product of the vectors A and B.
Alternatively, you can calculate the dot product A
• B with the syntax dot(A,B).

Multiply B times A.

C = B*A

C =
1 1 0 0
2 2 0 0
3 3 0 0
4 4 0 0

The result is a 4-by-4 matrix, also called the outer
product of the vectors A and B.
The outer product of two vectors, A ⊗ B,
returns a matrix.

Product Array, returned as a scalar, vector, or matrix. Array C has
the same number of rows as input A and the same
number of columns as input B. For example, if A is
an m-by-0 empty matrix and B is a 0-by-n empty
matrix, then A*B is an m-by-n matrix of zeros.