Options A, B are the properties of the group
C. $(ab) \neq a^{-1} b^{-1}$ for $(ab)^{-1} = b^{-1} a^{-1}$
$\qquad \quad = (ab).b^{-1}.a^{-1} = e$
$\qquad \quad = a(bb^{-1})a^{-1}$
$\qquad \quad = aea^{-1}$
$\qquad \quad = aa^{-1}$
$\qquad \quad = e$
Thus option C is wrong.
D. For monoid inverse does not exist.
$\therefore$ Therefore left cancellation property not possible.
