The binary operation on the set of real numbers is defined by m*n = mn2 m n 2 for all m, n ∈ ∈ R. If the identity element is 2, find the inverse of -5

The binary operation on the set of real numbers is defined by m*n = $\frac{mn}{2}$ for all m, n $\in$ R. If the identity element is 2, find the inverse of -5

Answer Details

m $\propto$ n = $\frac{mn}{2}-a$
Identify = e = 2
a $\propto$ a-1 = e
a $\propto$ a-1 = 2
-5 $\propto$ a-1 = 2
$\frac{-5\times a^{-1}}{2}=2$
$a^{-1}=\frac{2\times 2}{-5}$
$a^{-1}=-\frac{4}{5}$