Where did I make a mistake in expanding the determinant?

Question

I want to work on the left determinant to find the last one. I did as follows but, the machinery way resulted it $(+2/b)$ while I got $(-2/b)$ as coefficient. May I ask you what is my probable mistake? Thank you!

$$\begin{vmatrix} b+a&1&0 \\ -b-1&-1&-2a \\-a-b&-1&2b \end{vmatrix}=(1/b)\begin{vmatrix} b+a&b&0 \\ -b-1&-b&-2a \\-a-b&-b&2b \end{vmatrix}=(-2/b)\begin{vmatrix} b+a&b&0 \\ b+1&+b&a \\-a-b&-b&b \end{vmatrix}=$$

$$(-2/b)\begin{vmatrix} -a&b&0 \\ -1&+b&a \\a&-b&b \end{vmatrix}$$‎

Answer 1

At the end you should multiply again by $-1$ taking $2/b$ in front.

Answer 2

In the last passage you summed the second column to the first one and then multiplied the first one by $-1$ (or, in other words, you substituted $C_1\to -C_1-C_2$) but you did not update the coefficient accordingly.