Doubt from matrices

Please help me out with this question
image

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

1 Like

image
image

Sir , How is this related to this question ?
Well thanks for teaching me something new

1 Like

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