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We studied the line emission from CH3CN and its deuterated isotopologue CH$_2$DCN towards the prototypical Class I object SVS13-A, where the deuteration of a large number of species has already been reported. Our goal is to measure the CH$_3$CN deuteration in a Class I protostar, for the first time, in order to constrain the CH$_3$CN formation pathways and the chemical evolution from the early prestellar core and Class 0 to the evolved Class I stages. We imaged CH2DCN towards SVS13-A using the IRAM NOEMA interferometer at 3mm in the context of the Large Program SOLIS (with a spatial resolution of 1.8"x1.2"). The NOEMA images have been complemented by the CH$_3$CN and CH$_2$DCN spectra collected by the IRAM-30m Large Program ASAI, that provided an unbiased spectral survey at 3mm, 2mm, and 1.3mm. The observed line emission has been analysed using LTE and non-LTE LVG approaches. The NOEMA/SOLIS images of CH2DCN show that this species emits in an unresolved area centered towards the SVS13-A continuum emission peak, suggesting that methyl cyanide and its isotopologues are associated with the hot corino of SVS13-A, previously imaged via other iCOMs. In addition, we detected 41 and 11 ASAI transitions of CH$_3$CN and CH2DCN, respectively, which cover upper level energies (Eup) from 13 to 442 K and from 18 K to 200 K, respectively. The derived [CH2DCN]/[CH3CN] ratio is $\sim$9\%. This value is consistent with those measured towards prestellar cores and a factor 2-3 higher than those measured in Class 0 protostars. Contrarily to what expected for other molecular species, the CH3CN deuteration does not show a decrease in SVS13-A with respect to measurements in younger prestellar cores and Class 0 protostars. Finally, we discuss why our new results suggest that CH3CN was likely synthesised via gas-phase reactions and frozen onto the dust grain mantles during the cold prestellar phase.