Symbols don't seem to have a matrix property, but you can try to use the BBAccumRotation tag, as described throughout this thread:
many thanks for pointing me in this direction. It seems that rotation and probably scaling can be deduced from that tag value. However, a simple mirror operation does not leave any traces (the width is still positive)
On the other hand, it seems that I can change a symbolItem's symbol while preserving the matrix. I hope that I can use this property to solve my problem
If you are wanting to replace items inside a transformed symbol, you may be able to accomplish this via Envelope Distort as well.