Show that the set of real diagonal (n by n) matrices (with non-zero diagonal elements) represent a group under matrix multiplication

We must show that the set satisfies the group requirements: Identity, Closure, Associativity and Invertibility.Identity: Contains identity matrixAssociativity: Follows from the rules of matrix multiplicationInvertibility: As none of the diagonal elements are non zero, if the reciprocal of each diagonal element is taken, the inverse can be obtainedClosure: Can show by example of multiplying two general matrices

NP
Answered by Nishil P. Further Mathematics tutor

2319 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

By using an integrating factor, solve the differential equation dy/dx + 4y/x = 6x^-3 (6 marks)


Given that p≥ -1 , prove by induction that, for all integers n≥1 , (1+p)^k ≥ 1+k*p.


Prove by induction that 2^(6n)+3^(2n-2) is divsible by 5. (AS Further pure)


What is sin(x)/x for x =0?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences