Question

is this an elementary matrix?
1 0
-5 1
if it is can you explain why it is?

Answer 1

It is an elementary matrix. From Wikipedia:

"In mathematics, an elementary matrix is a simple matrix which differs from the identity matrix by one single elementary row operation."

"Elementary Row Operations.

1. Interchange two rows.
2. Multiply a row with a nonzero number.
3. Add a row to another one multiplied by a number."

The identity matrix is
1 0
0 1

So if you add the top row, multiplied by -5 to the bottom row you get your matrix. Which makes it an elementary matrix.