Finding composite elementary matrix by applying operations to identity matrix. With homogeneous coordinates. Why are most right 0 values affected?

Question

I trying to find the 3 x 3 elementary matrix that produces the described composite 2D transformation, using homogeneous coordinates.

1. Translate by (−3,2)
2. then scale the x-coordinate by 0.2 and the y-coordinate by 1.2

What I did:

I used a 3x3 identity matrix as a basis, applied the translation by adding -3 to the top row, x co-ordinate and +2 to the 2nd row to get translation followed by scaling x and y coordinates:

$\begin{bmatrix}((1-3)*0.2=0.4) & 0&0\\0&((1+2)*1.2=3.6)&0\\0&0&1\end{bmatrix}$

It turns out completely wrong, this is the answer:

My intuition was to isolate the transforms to the first two rows which are the x and y coordinates of the matrix, but clearly, my answer is completely off.

Based on the answer, we seem to add -3 and 2 to the first row, third value and second row, third value respectively before scaling. Why does translation affect those values in a matrix?