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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

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