a small square loop of wire of side L is placed inside a large square loop of wire of wire of side l(l>>L) .the loops are coplanar and their centers coinced . the mutual indutance of the system is proportional to

mutual inductance (area of smaller loop)× (magnetic field at center due to bigget loop ) ÷(current flowing in external loop). Now area of smaller loop is directly proportional to (L)², and magnetic field at center due to bigget loop is inversely proportional to l. Hence L²/l. Please do approve my answer if correct