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
3289 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0. Find dy/dx and d^2y/dx^2. Verify that C has a stationary point when x = 4
Integrate f(x) = 1/(1-x^2)
How do you find the determinant of a matrix?
A rectangular hyperbola has parametric equations x = 4t, y = 4/t , (z non 0). Points P and Q on this hyperbola have parameters t = 1/4 and t = 2. Find the equation of the line l which passes through the origin and is perpendicular to the line PQ.