Please help me out with this question

# Doubt from matrices

Is the answer 0 ?

Yes ! Please show the solution

Do you know what is a rank of a matrix ? And the properties associated with it ?

I have solved it with the help of that , so if you know about it I’ll explain my solution to you , else you’ll need to understand the what rank is and what are its properties

No sir,I don’t know what rank is , can you please explain it to me

Sir , How is this related to this question ?

Well thanks for teaching me something new

See AB is a 2X2 matrix so it’s rank is 2

And according to the property mentioned above , rank of AB = rank of BA

And hence rank of BA is also 2 but BA is a 3x3 matrix , and we know that since rank of BA is 2 therefore det of any it’s matrix with order > 3 will be zero

Hence |BA|=0

Thanks a lot for your unique approach @ Shwetanshu_2018 . Is there any other method also to solve this?

Your welcome !

And maybe there would be some other approach also , but I’m not able to think of any other method as of now .