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You just need to learn how to substitute numbers for letters,
which is very easy to do.  All you do is:

1. Put 0 or (0) everywhere there is an "a",
2. Put 3 or (3) everywhere there is a "b".
3. Put 4 or (4) everywhere there is a "c".
4. Put -2 or (-2) everywhere there is a "d".

So comparing the matrix



to your matrix,



then do the substituting in



and you will have:

  

which is the inverse of that matrix, unsimplified.

Now you only have to simplify everything:





Now distribute by multiplying the  by every 
element in the matrix.




Then simplify



Edwin