A 3x3 image kernel takes 9 multiplications and 8 or 9 additions for each pixel? I doubt because you have 9 multiplications and you are adding 9 numbers together, when using a 3x3 convolution matrix.

Adding 9 numbers: 1+2+3+4+5+6+7+8+9

We are performing 8 additions  as we repeat the operation of 'adding' 8 times (8 times a '+' sign).

We can say there are 9 additions as well, if you would accept a definition like: 0+1+2+3+4+5+6+7+8+9

But what does make more sense for computers: 8 adds or 9 adds?
As you have 9 terms to add together, your computer will perform 8 additions as each addition needs two inputs. So you have 9 multiplications and 8 additions.