Question

If the product of two non-zero matrices is a zero matrix, shown that both of them must be singular matrices.

Answer 1

Step-by-step explanation:

SOLUTION

Let each of the two matrices A and B, be a non-zero matrix of n*n order.

Given AB = O

It is to prove that | A | = 0 and | B | = 0.

Let | B | ≠ 0. Then B-¹ exists.

Hence,

From given equation AB = O, we get AB B-¹ = O => AI = O => A = O.

But A is not a zero matrix, therefore | B | is necessarily = O

Answer 2

Step-by-step explanation:

Define valence electrons.

the product of two non-zero matrices is a zero matrix, shown that both of them must be singular matrices.