Question

own example for A&B such that AB≠BA​

Answer 1

Answer:

Step-by-step explanation:

It simply isn't true that AB=BA, except in very special cases, such as if both A and B are diagonal.

For instance, for general 2×2 matrices A=$\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] \left$and B=$\left[\begin{array}{ccc}r&s\\t&u\\\end{array}\right] \left$ we have

AB=$\left[\begin{array}{ccc}ar+bt&as+bu\\cr+dt&cs+du\\\end{array}\right]$

while

BA=$\left[\begin{array}{ccc}ar+cs&br+ds\\at+cu&bt+du\\\end{array}\right]$

and you can clearly see that there are loads of choices for a,b,c,d,r,s,t,u that makes these two matrices different.