A=matrix(QQ, 3, 3, [2,1,3,1,2,1,1,1,2])
B=matrix(QQ, 3, 3, [3/2,1/2,-5/2,-1/2,1/2,1/2,-1/2,-1/2,3/2])
AB=A*B
BA=B*A
Bt=B.transpose()
At=A.transpose()
Ai=A.inverse()
I=identity_matrix(3)
print AB==BA==I #checking (inverse matrix of A)=B
print At.inverse()==Ai.transpose() #checking inverse matrix of transpose of A= transpose matrix of inverseof A