CBSE Class 12-science Answered

Dear Student,

The solution to your problem is as follows -

Let A and B be two non-empty (or non-null) matrices.

By the hypothesis of the question, AB=0

Now, Assume that A is non-singular.

=> A^-1 exists.

Therefore, multiply both sides of equation by A^-1

=> A^-1AB=0

=> B=0

But this is a contradiction to the fact that B is non-empty matrix. Hence A can't be non-singular matrix.

Similarly, assume B to be non singular.

=> B^-1 exists.

Multiply both sides by B^-1,

=> ABB^-1=0

=> A=0

Again, this is contradiction to the fact that A is non-empty. Therefore, B can't be non-singular.

Regards Topperlearning.