Internal Memo

XEROX
To    From
McIsaac    Arnon
    PARC/CSL





Subject    Date
Matrix multiplication    July 17, 1987


Testing commutativity of matrix multiplication
Consider the product of two general 2 x 2 matrices:


X
which is
X

Now consider the product in the opposite order:
X
which is
X

A direct check tells us that the first product is not equal to the second.  Let's determine the conditions under which they are 
equal by subtracting one from the other, setting equal to zero, and solving:

X
Let's try solving the two equations in the first row for a and b in  terms of the other indeterminates:
X  and X ,
which give us the conditions under which the product is commutative.