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should I use real numbers ??

I have a maths question which reads:

Let M be the set of all real 2 * 2-matrices of the form:

(a 0)

(0 b)

Show that this set of matrices is closed under matrix multiplication, and that matrix multiplication is commutative on this set.

Should I use real numbers to solve this problem or use what the question gave??

Re :should I use real numbers ??

I forgot to mention.. the attached image is the matrix given in the question.

Re: should I use real numbers ??

Quote:

Originally Posted by

**CaptainBlack** Are you asking if you should replace a snd b with particular numbers?

If so the answer is no.

That M is closed under matrix multiplication is equivalent asking you

to prove that for any real numbers a, b, c, d, there exist two real numbers

e,f such that:

Code:

`[a 0] [c 0] = [e 0]`

[0,b] [0 d] [0 f]

and that multiplication is comutative on M equivalent asking you

to prove that for any real numbers a, b, c, d that:

Code:

`[a 0] [c 0] = [c 0] [a 0]`

[0,b] [0 d] [0 d] [0 b]

RonL

Thankyou for your help.

I believe I've got it now..

Here's how I'm going to completely answer the question:

Code:

`Let a,b,c,d,e,f be real numbers:`

[a 0] [c 0] = [e 0]

[0 b] [0 d] = [0 f]

.: M is closed under matrix multiplication because the product of two M members is also in the M set.

Let A = [a 0]

[0 a]

B = [b 0]

[0 b]

AB = [ab 0]

[0 ab]

BA = [ab 0]

[0 ab]

AB = BA

.: matrix multiplication is commutative on this set.