profile-img
Sudhanshu Ranjan posted an Question
August 27, 2020 • 05:13 am 30 points
  • CSIR NET
  • Mathematical Sciences

Prove that there are no n×n matrix x and y such that xy - yx = i, where i is n×n identity matrix and n is positive integer

Prove that there are no n×n matrix X and Y such that XY - YX = I, where I is n×n identity matrix and n is positive integer

2 Answer(s) Answer Now
  • 0 Likes
  • 2 Comments
  • 0 Shares
  • Shashi ranjan sinha best-answer

    Here I used the two important results related to trace of the matrices.... tr (A +B) = tr A + tr B and tr(AB) = tr(BA)

whatsapp-btn

Do You Want Better RANK in Your Exam?

Start Your Preparations with Eduncle’s FREE Study Material

  • Updated Syllabus, Paper Pattern & Full Exam Details
  • Sample Theory of Most Important Topic
  • Model Test Paper with Detailed Solutions
  • Last 5 Years Question Papers & Answers