Math, asked by srinivas55ak55, 1 year ago

own example for A&B such that AB≠BA​

Answers

Answered by bruuxna
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] \leftand 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.

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