Linear Algebra Matrix with Elementary Row Operations

[lina29]

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

 

[Mark44]

Of the three elementary row operations, only one of them changes the value of the determinant of the matrix. Do you know which one this is?

Since you end up with the identity matrix (det(I) = 1), you can pick out the row operations that affect the determinant, to get the determinant of your starting matrix.