# Linear Algebra Matrix with Elementary Row Operations

## Homework Statement

The 3x3 matrix A is transformed into I by the following elementary row operations
R1+2R3 -> R1
R2+2R3 ->R2
2R2 ->R2
R1 <->R2
2R3 ->R3

Find det(A)

## Homework Equations

I assumed to start off with the problem since I was going backwards from I to A. I would do the opposite of each row operation ie
2R3-R1 ->R1
2R3-R2 ->R2
(1/2)R2 ->R2
R1 <->R2
(1/2)R3 ->R3

## The Attempt at a Solution

By finding the det(A) I got -1/4. I'm confused on if I messed up on the row operations. When I did this problem without using the backwards row operations I got -4 which was also wrong. I'd appreciate any help

Thanks