code: public static Matrix arbitrariness(Matrix source, Matrix inverse) {
  		Matrix intermediate = inverse.mtimes(source);
  		return DenseDoubleMatrix2D.Factory.eye(intermediate.getRowCount(),
  				intermediate.getColumnCount()).minus(intermediate);
  	}
docs: Calculate the arbitrariness of the solution. This is a way to find out
  how unique the existing inverse is. The equation is here: A * x = b And
  the solution is: x = A12 * b + an arbitrariness which could be infinite,
  but will follow a general pattern. For instance, if the solution is a
  line, it could be anchored in the Y at any arbitrary distance. If the
  solution is a plane it could be arbitrarily set to any place in perhaps
  two different dimensions.
  
  The arbitrariness is calculated by taking the difference between the
  complete inverse times the original and subtracting the generalized
  inverse times the original matrix. That's the idea, here's the formula:
  
  x = A12 * b + (I - (A12 * A)) * z The z is a completely arbitrary vector
  (you decide that one). The product (A12 * A) could be the Identity
  HusoMatrix, if the solution is unique, in which case the right side drops
  out: (I - I) * z
  
  Again, it's a lot easier to refer to the http://aktzin.com/ site for the
  description and a different way to get this information.
  
  @return the matrix (I - (A12 * A))