Let O denote the matrix [ 0 0 0 0 ] . Find 2 × 2 matrices A and B such that A ≠ O and B ≠ O but A B = O .

Find 2 × 2 matrices A and B such that A≠O and B≠O, but AB = O.

Given information:

Let O denote the matrix [0000].

Calculation:

We have O=[0000]

For example, let us choose the following two 2 x 2-matrices:

A=[ 1 0 1 0]≠OB=[ 0 0 1 1]≠O

The first matrix has dimensions 2 × 2 and the second matrix has dimension 2 × 2. Since the inner dimensions are equal, we can multiply the matrices. Moreover, the product should be a 2 × 2-matrix.

Multiply the rows of the first matrix with the columns of the second matrix (adding the products of the corresponding elements):

AB=[ 1 0 1 0][ 0 0 1 1]<