  We study the characteristics of quark matter under the influence of a
background magnetic field with anomalous magnetic moment (AMM) of quarks at
finite temperature and quark chemical potential in the framework of Polyakov
loop extended Nambu Jona-Lasinio (PNJL) model. In presence of a magnetic field,
the speed of sound and isothermal compressibility become anisotropic with
respect to the direction of the background magnetic field, splitting into
parallel and perpendicular directions with respect to the magnetic field.
Though the qualitative nature of parallel and perpendicular components of
squared speed of sound appear similar, they differ in magnitude at lower values
of temperature. The parallel and perpendicular components of isothermal
compressibility decrease with increasing temperature, indicating a trend
towards increased incompressible strongly interacting matter. On inclusion of
the AMM of quarks, the perpendicular component of isothermal compressibility
becomes greater than the parallel component. Additionally, we investigate the
quark number susceptibility normalized by its value at zero magnetic field,
which may indicate the presence of magnetic fields in the system.
