print" if A*C=A*D doesn't necessarily imply C=D(even when A!=0)"
var('A,C,D')  #initializing three matrices
A=matrix([[1,1],[2,2]])
C=matrix([[2,1],[2,2]])
D=matrix([[3,0],[1,3]])
print A
print C
print D
print A*C  # multipling A and C in this order
print A*D  # multipling A and D in this order