Many mathematical formulations of Quantum Mechanics have been developed with the goal of describing particular phenomena in a convenient way. The wave formulation is useful for capturing the phase behavior of quantum systems, characteristic of the wave-particle duality and matrix mechanics lends itself to describing quantum systems using matrix algebra to capture the non-commutative nature of measurements. While these two formulations are the most commonly taught, due in large part to their mathematical approachability, there exist other formulations more clearly describe other phenomena. The Path-Integral formulation of Quantum Mechanics succinctly captures the time evolution of quantum systems by generalizing the Principle of Least Action, arguably the most fundamental principle undergirding Classical Mechanics. Path-Integral Quantum Mechanics is centered on an object called the Propagator, K(x'',t'';x',t'), which is a matrix element of the time evolution operator from t' to t'' from an initial state x' to a final state x''. With clever use of matrix calculus, we will find that the Propagator is closely related to the Classical Lagrangian and acting it against some initial quantum state results in an integral over all paths weighted by the complex exponential of the Lagrangian. Application uses the Maple Quantum Chemistry Toolbox.