Elementary matrix

Hey there kiddo! Today, we're going to learn about something called an elementary matrix. Now, a matrix is like a special box that has numbers inside of it. It might look like this:

```
1 2 3
4 5 6
7 8 9
```

Each number in a matrix is in a special spot, called a "row" and a "column". So, in this example, the number 2 is in the first row and second column. The number 5 is in the second row and second column.

Now, an elementary matrix is a special kind of matrix that helps us do some cool math things. It looks like a regular matrix, but with some special rules.

For example, let's say we want to multiply a matrix by an elementary matrix. This is kind of like doing a special dance with the numbers inside the matrix. The dance makes some of the numbers bigger or smaller, or switches them around.

Why would we want to do this? Well, sometimes when we're doing math problems, we want to change a matrix in a certain way. Maybe we want to make a certain number bigger or smaller, or change the order of the numbers. An elementary matrix helps us do this in a really easy way.

So, to sum it up: an elementary matrix is a special box of numbers that lets us do cool math things with other matrices. It's like a dance routine that changes the numbers in a matrix in a certain way, making it easier to solve math problems. How's that for an explanation?