nilpotent matrix

Which of these definitions is correct.
ML khanna says
a square matrix is called nilpotent matrix if A^k=O,where 'k' is a positive integer,smallest value of k is called index of nilpotent matrix

SK goyal in Arihant algebra says
a square matrix A is called nilpotent matrix of order 'm' if A^k=O,A^k-1≠O,where 'k' is positive integer,O is null matrix & 'k' is order of nilpotent matrix A