Thanks to a friend of mine, Dick Ploeg, I was directed to a location where to find more info:
www.conam.info/kentekens/provincienummers, a general site on these numbers.
www.groningerkentekens.nl, specific site with the numbers in the province of Groningen.

This system of number plates (which were plates belonging to the individual, not the car) was the first system in the Netherlands, and existed from 1906 until 1951, 1956 being the year that the last numbers were changed to license plate numbers (belonging to the car, not the individual).

These numbers all started with a letter, indicating the province. "A" being for the province of Groningen.

Using the site above, it was easy to find that the number was issued to Hendericus Bulk, living in the city of Groningen, and being a Fish merchant. Dick Ploeg could inform me that the number was issued in 1925. Of course, using the name and the fact that he was a Fish merchant, gives more background info: Hendericus Bulk, also called Henderikus Bulk, was born March 13, 1907, and died relatively young, aged 50, on June 5, 1957. Thus; he received the number aged 18 years!

Unluckily, no photographs of the actual car(s) exist. I did find some info about Harm (his father) and Hendericus. The photo on the right show the interior of the fish shop, and was taken in around 1920. Hendericus is the boy in the corner (still too young to drive a car), his mother Trijntje Talens helping a customer. The shop was located on the Zuiderdiep 43, Groningen.

More info can be found here: groninganus.wordpress.com/2008/04/18/het-vis-imperium-van-de-familie-bulk/

As I did not know of the site before, I searched for my family, and found out that the number plate for my grandfather Roelof Horst was A-23022, the website even shows a photograph of my grandparents, posing proudly in front of the house, the Chevrolet also shown. My grandfather was a blacksmith, though he also had a Caltex petrol station, and his car could be hired (or sometimes was used as a taxi). The photograph was taken in 1955 (still the old number on the car!), Dorpsweg 13, in the vilage of Garmerwolde, a bit north to the city of Groningen.