this means that A is equal to its inverse. So you may write the expression of and deduce 4 equations from the identification of it with A. It remains to solve these equations
I need to find all 2x2 matrices A,
(a b)
(c d)
such that A^2=I2, the 2x2 identity matrix.
Just to flesh out what tah said:
you have
now, compute the matrix product on the left hand side, then equate corresponding components to get your 4 equations that tah spoke of. solve this system for your solution