reserve i,n for Nat,
  K for Field,
  M1,M2,M3,M4 for Matrix of n,K;

theorem
  M1 is Nilpotent & n>0 implies M1@ is Nilpotent
proof
  assume that
A1: M1 is Nilpotent and
A2: n>0;
  len M1=n & width M1=n by MATRIX_0:24;
  then M1@*M1@=(M1*M1)@ by A2,MATRIX_3:22
    .=(0.(K,n))@ by A1
    .=(n,n)-->0.K by MATRIX_6:20
    .=0.(K,n);
  hence thesis;
end;
