The procedure for MATZ penetration is published in the AIP (ENR 2-2-2-3-1. The hyperlink is here:
http://www.ais.org.uk/aes/pubs/aip/pdf/enr/2020203.PDF ) * In brief, observance of a MATZ by civil aircraft is not mandatory. However, observance of any associated ATZ is. As is also mentioned in other posts on this thread, there are other good (both legal and simple good common sense) reasons why transiting traffic must speak to the MATZ controller.
Any instructor who is not aware of the requirements regarding MATZ should rectify the gap in their knowledge, pronto!
P
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