Here is my current issue.
Our teacher asked a question related to the finding of an inverse of 2. Here is all of the given information:
Define "a cross b" as such: a ☢ b = ab + (a + b). Use this new operation to evaluate the following. Find the "cross" inverse of 2.
Here is the work that I have currently done:
2 ☢ x = -1
2x + (2 + x) = -1
3x + 2 = -1
3x = -3
x = -1
Any help would be greatly appreciated.
First, you need to find the neutral element. It's not $-1$, it's zero, since $$a\otimes 0=a0+a+0=a$$
Now, to find the inverse of $2$, you want $2\otimes x=0$, and then continue as you have $2x+2+x=0$, so $3x=-2$ or $x=-\frac{2}{3}$.