Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Examples

Example 1

Example 2

Example 3 Important

Example 4

Example 5 Important

Example 6

Example 7

Example 8

Example 9

Example 10

Example 11 Important

Example 12

Example 13 Important

Example 14

Example 15

Example 16 Important

Example 17

Example 18 Important

Example 19

Example 20 Important

Example 21

Example 22 Important

Example 23 Important

Example 24 Important You are here

Example 25

Question 1 Deleted for CBSE Board 2024 Exams

Question 2 Important Deleted for CBSE Board 2024 Exams

Question 3 Important Deleted for CBSE Board 2024 Exams

Chapter 3 Class 12 Matrices

Serial order wise

Last updated at June 8, 2023 by Teachoo

Example 24 If A and B are symmetric matrixes of the same order, then show that AB is symmetric if and only if A and B commute, that is AB = BA. Given A & B are symmetric matrix i.e. A’ = A B’ = B We need to show AB is symmetric if and only if A & B commute (i.e. AB = BA) i.e. we need to show If AB is symmetric, then A & B commute (i.e. AB = BA) and If A & B commute (i.e. AB = BA), then AB is symmetric Proving Forward part If AB is symmetric then A & B commute Given AB is symmetric i.e. (AB)’ = AB B’A’ = AB BA = AB Hence A & B commute. Hence proved Proving backward part If A & B commute, then AB is symmetric Given A & B commute i.e. AB = BA We need to show AB is symmetric i.e. we need to show (AB)’ = AB Taking (AB)’ = B’A’ = BA = AB So, (AB)’ = AB Hence, AB is symmetric Hence proved Therefore, AB is symmetric if and only if A and B commute, i.e. AB = BA.