This is one of several "Agent Smith" ties worn by the cloned agent during the large fight scenes. This particular one was not worn by Hugo Weaving, but by the many double stand ins dressed as him.
These items were used in Matrix Reloaded and Matrix Revolutions as the movies were filmed back to back and are instantly recognizable as the infamous Agent Smith.
Made in Australia, where the movies were filmed, features an all metal pin clasp and the neck section is velcro-ized to allow actors put and remove it quickly and avoid the hassle to knot it every time.
COA: ScreenUsed
Image 2: Hugo Weaving as the Agent Smith and his clones on the Matrix trilogy wearing this particular tie style...