matrices ever be communitative? [Solved!]

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

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

X

Great answer! Thanks