For the matrices A and B, verify that (AB)' =B'A', where A=⎡⎢⎣1−43⎤⎥⎦,B=[−1 2 1]
Here, AB=A=⎡⎢⎣1−43⎤⎥⎦[−1 2 1]=⎡⎢⎣−1214−8−4−363⎤⎥⎦(AB)′=⎡⎢⎣−1214−8−4−363⎤⎥⎦=⎡⎢⎣−14−32−861−43⎤⎥⎦......(i)
Also, B′A′=[−1 2 1]′⎡⎢⎣1−43⎤⎥⎦=⎡⎢⎣−121⎤⎥⎦[1 −4 3]=⎡⎢⎣−14−32−861−43⎤⎥⎦.........(ii)
From Eqs. (i)and (ii), we find that (AB)'=B'A'.