IMO it is a true skill in maths to be able to just take one side (LHS or RHS) and turn it into the other using allowed manipulations and assumptions in the case of induction.
As for how your school marks it well looking back at previous tests in my school, before tests are done solutions are written up and they have marking guidelines and your teachers
are forced to make accordingly to those guidelines. If you're method is not valid according to the guidelines then you can lose the marks depending on how leanient your school is.
I remember in one of my 4u tests i did something extravogent and these was a bit of an arguement between my teacher and the head math teacher whether or not to give me the
mark as it was, lets say, inventive. However, if you care about my little story i did get that mark and it made no difference as I was the only one doing 4u.