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

Related Further Mathematics A Level answers

All answers ▸

Prove by induction that 1^2 + 2^2 + 3^2 + . . . + n^2 = (1/6)n(n+1)(2n+1)


Show that the points on an Argand diagram that represent the roots of ((z+1)/z)^6 = 1 lie on a straight line.


Prove that (AB)^-1 = B^-1 A^-1


A golf ball is hit from horizontal ground with speed 10 m/s at an angle of p degrees above the horizontal. The greatest height the golf ball reached above ground level is 1.22m. Model the golf ball as a particle and ignore air resistance. Find p.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences