  We study the dynamics of test particle and stability of circular geodesics in
the gravitational field of a non-commutative geometry inspired Schwarzschild
black hole spacetime (NCSBH). The coordinate time Lyapunov exponent
($\lambda_{c}$) is crucial to investigate the stability of equatorial circular
geodesics of massive and massless test particles. The stability or instability
of circular orbits are discussed by analysing the variation of Lyapunov
exponent with radius of these orbits for different values of non-commutative
parameter ($\alpha$). In the case of null circular orbits, the instability
exponent is calculated and presented to discuss the instability of null
circular orbits. Further, by relating parameters corresponding to null circular
geodesics (i.e. angular frequency and Lyapunov exponent), the quasinormal modes
(QNMs) for a massless scalar field perturbation in the eikonal approximation
are evaluated, and also visualised by relating the real and imaginary parts.
The nature of scalar field potential, by varying the non-commutative parameter
($\alpha$) and angular momentum of perturbation ($l$), are also observed and
discussed.
