If A and B are 2 matrices of any order such that AB=O and A is non-singular then

a]  B=O

b]  B is non-singular

c]  B is singular

d]  B=A

       The ans is B=0.what i want to know is why option c is wrong.please help

hiiii

 

see, AB = 0

 

so, clearly |AB| = 0

      

          or, |A||B| = 0  

 

but |A|  0 , thus |B| = 0

 

Now B has to be singular ..

 

But see the issue is that AB = 0 and A is non-singular ..

 

so, A^-1 exists.

 

and thus, A^-1.AB = A^-1.0

 

or B = 0

 

if the question has only one correct answer then obviously we need to mark B = 0

 

the fact that B is singular will follow from B = 0. We should always mark the superset if it is there in the choices.

 

I hope it is clear.

 

cheers

hiiiii everyone,

   hurrayy !!!!!!!! at last i have got the answer which i was looking for.it striked me suddenly.here the question asked is matrix.but for singular or non -singular it should be a determinant .for example,consider a matrix A of order 3 by 3 and a matrix B of order 3 by 4 and by the given condition A is non -singular.but B cant be singular as the number of rows is not equal to number of columns and so the only possibility is B=0.or in another words B need not be a determinant.

 

and as puneet sir has said ,thus,B=0 is the  super set.i think puneet sir might have said it in the same meaning ,but i couldnt understand.

 

if any body has questions in matrix please post here.thanks....

 

cheers!