Let M(n, R) denote the set of all n × n matrices over R. Define a relation on M(n, R) as follows: for A, B M(n, R), A B iff there exists an invertible matrix P such that P 1AP = B. Show that is an equivalence relation.

#SET

155 Views

Let M(n, R) denote the set of all n × n matrices over R. Define a relation on M(n, R) as follows: for A, B M(n, R), A B iff there exists an invertible matrix P such that P 1AP = B. Show that is an equivalence relation.

Latest: SET Result link 2024 | Liberal Arts & Sciences Complete Guide

Also Check : Save up to ₹2000 on TOEFL, GRE & PTE through ApplyShop

Akash Girde 7th Nov, 2020

Answer

Answer Later

Report

Answer (1)

Anuj More 8th Nov, 2020

Dear candidate,

Kindly know that is a long mathematical question. We can't prove the sum because we are limited by our answering options. You can search the question on internet to get a better understanding of this problem through detailed step by step equations. There are various portals on internet which will make this question easy for you to understand.

Thanks.

Like Share

Know More About

Symbiosis Entrance Test

Eligibility | Application | Admit Card | Result | Preparation Tips | Dates | FAQs

Get Updates

Related Questions

show that each of the relation R in the set A={x belongs to z:0 is less than or equal to x is less than or equal to 12} given by a. R={(a, b):|a-b|is a multiple of 4} b. R={(a, b):a=b}is an equivalence relation.

696 Views

For x, y R define x y to mean that |x| = |y|. Prove that is an equivalence relation in R. Describe [0], [5], and [5].

115 Views

show that the relation R defined in set A = {1,2} as R = {(1,2)} is transitive

912 Views

show that the number of equivalence relation in the set(1,2,3) containing (1,2) and (2,1) is two

321 Views

if E1 E2 and E3 are equivalence classes with respect to a relation R in set A then elements of which equivalence classes are related to each other

54 Views

Applications for Admissions are open.

UPES B.Tech Admissions 2025

Apply

Ranked #42 among Engineering colleges in India by NIRF | Highest CTC 50 LPA , 100% Placements

Pearl Academy B.Des Admission...

Apply

No. 1 Design & Fashion Institute by ASSOCHAM, India Today, Outlook and The Week rankings

UPES B.Des Admissions 2025

Apply

Ranked #46 amongst Universities in India by NIRF | Ranked #1 in Academic Reputation in India by QS World University Rankings

UPES | BBA Admissions 2025

Apply

#41 in NIRF, NAAC ‘A’ Grade | 100% Placement, up to 30% meritorious scholarships

Pearl Academy BBA 2025

Apply

No. 1 Design & Fashion Institute by ASSOCHAM, India Today, Outlook and The Week rankings

Integral University B.Tech Ad...

Apply

NAAC A+ Accredited | Highest CTC 12 LPA | Scholarships Available

View All Application Forms

Upcoming Exams

Karunya University Entrance Exam - (KEE)

Application Date: 14 Nov, 2024

Application Process Counselling Process

Vit Engineering Entrance Exam - (VITEEE)

Application Date: 4 Nov, 2024 - 31 Mar, 2025

Eligibility Criteria Application Process Exam Pattern Slot Booking Admit Card Result Counselling Process Preparation Tips Mock Test Books Question Paper

Undergraduate Common Entrance Examination For Design - (UCEED)

Application Date: 1 Nov, 2024 - 18 Nov, 2024

Eligibility Criteria Exam Pattern Application Process Admit Card Preparation Tips Result Answer Key Counselling Process Cutoff Question Paper

Footwear Design & Development Institute All India Selection Test - (FDDI AIST)

Application Date: 1 Nov, 2024 - 20 Apr, 2025

Eligibility Criteria Exam Pattern Counselling Process Application Process Admit Card Result

Lovely Professional University National Entrance And Scholarship Test - (LPU NEST)

B.Tech

Exam Pattern

Trending Articles around SET

You Maybe Interested In

Management colleges in India

Management colleges in India accepting SET

Management colleges in Pune accepting SET

Management colleges in Kompally accepting SET

Management colleges in Maharashtra accepting SET

Management colleges in Telangana accepting SET

Top Management colleges in India

Top Management colleges in India accepting SET

Top Management colleges in Pune accepting SET

Top Management colleges in Kompally accepting SET

Top Management colleges in Maharashtra accepting SET

Top Management colleges in Telangana accepting SET

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students

30,000+ Colleges

500+ Exams

1500+ E-books