We present high-precision photometry of eight separate transit events in the HAT-P-32 planetary system. One transit event was observed simultaneously by two telescopes of which one obtained a simultaneous multiband light curve in three optical bands, giving a total of 11 transit light curves. Due to the filter selection and in conjunction with using the defocused photometry technique, we were able to obtain an extremely high-precision, ground-based transit in the u band (350 nm), with an rms scatter of ≈1 mmag. All 11 transits were modelled using PRISM and GEMC, and the physical properties of the system calculated. We find the mass and radius of the host star to be 1.182 ± 0.041 M⊙ and 1.225 ± 0.015 R⊙, respectively. For the planet, we find a mass of 0.80 ± 0.14 MJup, a radius of 1.807 ± 0.022 RJup, and a density of 0.126 ± 0.023 ρJup. These values are consistent with those found in the literature. We also obtain a new orbital ephemeris for the system T0 = BJD/TDB 2 454 420.447187(96) + 2.15000800(10) × E. We measured the transmission spectrum of HAT-P-32 A b and compared it to theoretical transmission spectra. Our results indicate a bimodal cloud particle distribution consisting of Rayleigh-like haze and grey absorbing cloud particles within the atmosphere of HAT-P-32 A b.