0

Guest

Courses New

If A and B are symmetric matrices of the same order, prove that AB + BA is symmetric

If A and B are symmetric matrices of the same order, prove that AB + BA is symmetric

Grade:

1 Answers

Latika Leekha
askIITians Faculty 165 Points
9 years ago
A matrix A is said to be symmetric if A = AT
Now, A and B are symmetric matrices, so we have
A = AT
B = BT
Now consider,
(AB + BA)T = (AB)T + (BA)T
= BTAT + ATBT
= BA + AB
= AB + BA
Hence, the matrix (AB + BA) is symmetric.
Thanks & Regards
Latika Leekha
askIITians Faculty

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More