A=matrix([[1,2],[2,4]])
print A
B=matrix([[2,1,4],[3,1.5,6]])
print B
var('b,c')
M=matrix([[1,b],[c,b*c]])
print M
D=A*B
print D
E=A*M
print E
R=rank(D)
print R
T=rank(E)
print T