[SOLVED] Elementary matrix, restore to identity matrix

2. d)

find a row operation that will restore the given elementary matrix to an identity matrix.

1 0 -1/7 0
0 1 0 0
0 0 1 0
0 0 0 1

I cannot solve this. I think I have to find an row operation that will make -1/7 become a 0. Please help.

Am I allowed to multiply row I by 7 which gives

7 0 -1 0
0 1 0 0
0 0 1 0
0 0 0 1

then add row III to row I to get

7 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

then multiply row I by 1/7 to get

1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1


Correct?

Yes. but that's not a single row operation.

This can be done by: Add 1/7 times the third row to the first row.

(In fact, an "elementary" matrix is defined as one that is created by applying a single row operation to the identity matrix. Here, this is an elementary matrix because it can be created by applying "subtract 1/7 times the third row from the first row" and, of course, you get back to the identity matrix by doing the opposite- add 1/7 times the third row to the first row.

Gotcha. Thanks.