The primary objective of this article is to chase the mysterybehind the fourth order Kaprekar constant 6174 using the principles of Linear Algebra and to hunt the other ordered Kaprekar constants. Kaprekarconstant 6174 has been an interesting one with its own mystery for decades in the research field of Analytical Number theory. Many recreational and experimental Mathematicians have been studying this number for years. In this research paper an attempt has been made to trace the mystery behindthatKaprekar constant 6174 and other Kaprekar constants of other orders. The method discussed here ensures a way to hunt Kaprekar constants of any order. Furthermore the proof of the existence and uniqueness of third order Kaprekar constant has been proposed and this proof can be implemented to find the Kaprekar constants of any order if they exist.