The set \(\mathrm { G } = \mathbb { R } - \left\{ - \frac { 3 } { 2 } \right\}\) with the operation of \(x \bullet y = 3 ( x + y + 1 ) + 2 x y\) forms a group.
Determine the identity element of this group.
Determine the inverse of a general element \(x\) in this group.
Explain why the value \(- \frac { 3 } { 2 }\) must be excluded from \(G\) in order for this to be a group.