  Studying cool star magnetic activity gives an important insight into the
stellar dynamo and its relationship with stellar properties, as well as
allowing us to place the Sun's magnetism in the context of other stars. Only 61
Cyg A (K5V) and $\tau$ Boo (F8V) are currently known to have magnetic cycles
like the Sun's, where the large-scale magnetic field polarity reverses in phase
with the star's chromospheric activity cycles. ${\tau}$ Boo has a rapid
$\sim$240 d magnetic cycle, and it is not yet clear whether this is related to
the star's thin convection zone or if the dynamo is accelerated by interactions
between ${\tau}$ Boo and its hot Jupiter. To shed light on this, we studied the
magnetic activity of HD75332 (F7V) which has similar physical properties to
${\tau}$ Boo and does not appear to host a hot Jupiter. We characterized its
long term chromospheric activity variability over 53 yrs and used Zeeman
Doppler Imaging to reconstruct the large-scale surface magnetic field for 12
epochs between 2007 and 2019. Although we observe only one reversal of the
large-scale magnetic dipole, our results suggest that HD75332 has a rapid
$\sim$1.06 yr solar-like magnetic cycle where the magnetic field evolves in
phase with its chromospheric activity. If a solar-like cycle is present,
reversals of the large-scale radial field polarity are expected to occur at
around activity cycle maxima. This would be similar to the rapid magnetic cycle
observed for ${\tau}$ Boo, suggesting that rapid magnetic cycles may be
intrinsic to late-F stars and related to their shallow convection zones.
