You are Here: Home

# Question on Groups concerning matrices...

Announcements Posted on
Talking about ISA/EMPA specifics is against our guidelines - read more here 28-04-2016
1. Let M denote the set of real 2x2 matrices of the form where x and y are not both zero,

M=
Show that M is a group under matrix multiplication. (you may assume that matrix multiplication is associative)

I am just confused about something, I am trying to figure if for example this is multiplication of the form:

or if the operation has to be of the form

,

---------------------------

nevermind, i messed up on something really simple...
2. It's safe to assume that is a group since the question asks you to show that it is, it doesn't ask whether or not it is.

If your example of didn't work then you must have multiplied your matrices wrong.

The closure property is this: if then .

So suppose and , with and . Show that can be written in the form and that (where are in terms of ).

P.S.: To fix your LaTeX code, take the { symbols off the start of each of the lines.
3. (Original post by nuodai)
It's safe to assume that is a group since the question asks you to show that it is, it doesn't ask whether or not it is.

If your example of didn't work then you must have multiplied your matrices wrong.

The closure property is this: if then .

So suppose and , with and . Show that can be written in the form and that (where are in terms of ).

P.S.: To fix your LaTeX code, take the { symbols off the start of each of the lines.
Ah thanks, coding fixed now
I actually worked out 2x3 + (1x-2) as being 9 for some reason in my counterexample which is why it confused me :s but my counterexample actually does conform to the group rules

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: April 7, 2012
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### How to predict exam questions

No crystal ball required

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams