Ursu L.A.
Symmetric n-loops with the inverse property

It is proved that the matrix [I_ij], where the substitutions I_ij are defined by the equalities (e^i-1,x,e^j-i-1,I_ijx,e^n-j) = e is one of the inversion matrices of the symmetric n-IP-loop with an unique unit e. From this result it follows that the matrix [I_ij] is a unique inversion matrix of such loops of an odd arity.