How many methods are there to find the inverse of matrix?

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I am an undergraduate math student.
I have found in my books there are only $2$ or $3$ methods of finding the inverse of matrix which are possibly row transformation, Gauss-Jordan elimination and the general adjoint/determinant method.

What I am wondering is matrix seems to be a art which is developed and I guess is still developing time to time. Can anyone provide any other methods to find inverse of matrix ?

Also let me know which method is faster. Some reference links or books are expected.

Have a nice day.