IntMath Home » Forum home » Matrices and Determinants » matrices ever be communitative?

# matrices ever be communitative? [Solved!]

### 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?

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?

Great answer! Thanks

X

Great answer! Thanks

## Reply

You need to be logged in to reply.