Question

If A and B are square matrices of order 3, A is a non-singular matrix and AB = O, then the matrix B is ______.

Options

• unit matrix

• scalar matrix

• non-singular matrix

• null matrix

Answer 1

If A and B are square matrices of order 3, A is a non-singular matrix and AB = O, then the matrix B is null matrix.

Explanation:

Given: A and B are 3 × 3 matrices, A is non-singular (so A⁻¹ exists), and AB = O (zero matrix).

Multiply both sides by A⁻¹ on the left:

A⁻¹ (AB) = A⁻¹ O

(I)B = O

B = O

So, matrix B is the null matrix.