# matrices ever be communitative? [Solved!]

**Kimberly** 28 Nov 2015, 06:11

### My question

Can matrices ever be communitative? If so can you give an example?

Kim

### Relevant page

6. Matrices and Linear Equations

### What I've done so far

I've read the page above

X

Can matrices ever be communitative? If so can you give an example?
Kim

Relevant page
<a href="/matrices-determinants/6-matrices-linear-equations.php">6. Matrices and Linear Equations</a>
What I've done so far
I've read the page above

## Re: matrices ever be communitative?

**Newton** 29 Nov 2015, 09:18

Hi Kimberly

I think you mean "commutative".

Do you mean commutative over addition, or over multiplication?

The answer is yes for both.

First, consider ordinary numbers. If I add 0 to a number, in any

order, I get the same value:

`5 + 0 = 0 + 5`

Now for multiplication. If I multiply by 1, in any order, I get the same value:

`5 xx 1 = 1 xx 5`

Matrices can also work the same way.

If I add the "zero matrix" (one with zeros in every position) in any

order, I get the same value matrix:

Say we have 1x3 matrices, `A = [(2, 5, 3)]` and `O = [(0, 0, 0)]`

`A + O = O + A`

Now for matrix multiplication:

Say we have 3x3 matrices,

`A=[ (3, 6, 9), (4, 1, 6), (9, 3, 1)]`

and `I =` the identity matrix `= [(1, 0, 0), (0, 1, 0), (0, 0, 1)]`

Then `AI = IA`

There is more on this in the middle of this page:

4. Multiplication of Matrices

Regards

X

Hi Kimberly
I think you mean "commutative".
Do you mean commutative over addition, or over multiplication?
The answer is yes for both.
First, consider ordinary numbers. If I add 0 to a number, in any
order, I get the same value:
`5 + 0 = 0 + 5`
Now for multiplication. If I multiply by 1, in any order, I get the same value:
`5 xx 1 = 1 xx 5`
Matrices can also work the same way.
If I add the "zero matrix" (one with zeros in every position) in any
order, I get the same value matrix:
Say we have 1x3 matrices, `A = [(2, 5, 3)]` and `O = [(0, 0, 0)]`
`A + O = O + A`
Now for matrix multiplication:
Say we have 3x3 matrices,
`A=[ (3, 6, 9), (4, 1, 6), (9, 3, 1)]`
and `I =` the identity matrix `= [(1, 0, 0), (0, 1, 0), (0, 0, 1)]`
Then `AI = IA`
There is more on this in the middle of this page:
<a href="/matrices-determinants/4-multiplying-matrices.php">4. Multiplication of Matrices</a>
Regards

## Re: matrices ever be communitative?

**Kimberly** 30 Nov 2015, 01:31

Great answer! Thanks

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