Q. 805.0( 1 Vote )

# Fill in the blanks in each of theIf A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.

This is only possible if A and B commute.

Proof:

Given A and B are symmetric matrices,

A’=A ..(1)

B’=B ..(2)

Let AB is a Symmetric matrix:-

(AB)’=AB

Using Property (AB)’=B’A’

B’A’=AB

Now using (1) and (2)

BA=AB

Hence A and B matrix commute.

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
Determinants of Matrices of different order59 mins
Types of Matrices & Properties51 mins
Interactive Quiz on Matrices and Determinants41 mins
Determining a determinant63 mins
Test Yourself, Properties of Determinants30 mins
Interactive Quiz on Matrices & Determinants48 mins
Lecture on Product of Determinants58 mins
Interactive Quiz on Properties of Determinants43 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