function value = projection_random_determinant ( n, k, key )

%*****************************************************************************80
%
%% projection_random_determinant() returns determinant of a random projection matrix.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    12 May 2020
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer N: the order of A (default = 5 ).
%
%    integer K: the rank of the matrix.  (default = n-1); 
%
%    integer KEY: a positive integer that selects the data.
%    (default = 123456789).
%
%  Output:
%
%    real VALUE: the determinant.
%
  if ( nargin < 1 )
    n = 5;
  end

  if ( nargin < 2 )
    k = n - 1;
  end

  if ( nargin < 3 )
    key = 123456789;
  end

  if ( k == n )
    value = 1.0;
  else
    value = 0.0;
  end

  return
end

