# Show by an example that for A ≠ O, B ≠ O, AB = O.

We know that,

In order to multiply two matrices, A and B, the number of columns in A must equal the number of rows in B. Thus, if A is an m x n matrix and B is an r x s matrix, n = r.

We are given that,

A ≠ 0 and B ≠ 0

We need to show that, AB = 0.

For multiplication of A and B,

Number of columns of matrix A = Number of rows of matrix B = 2 (let)

Matrices A and B are square matrices of order 2 × 2.

For AB to become 0, one of the column of matrix A and other row of matrix B must be 0.

For example,  Check: Multiply AB. Multiply 1st row of matrix A by matching members of 1st column of matrix B, then sum them up.

(0, 1).(3, 0) = (0 × 3) + (1 × 0)

(0, 1).(3, 0) = 0 + 0 = 0 Similarly, let us do it for the rest of the elements.  Thus, this example justifies the criteria.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Triangular Matrices & operations on matrices58 mins  Types of Matrices & Properties51 mins  Determinants of Matrices of different order59 mins  Determining a determinant63 mins  Lecture on Product of Determinants58 mins  Know About finding the Adjoint & Inverse Of Matrix46 mins  Interactive Quiz on Properties of Determinants43 mins  Test Yourself, Properties of Determinants30 mins  Interactive Quiz on Matrices & Determinants48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 