Itr , 11 bytes

(1ä,1)#^M¡M

takes n as input, computes the n-th Fibonacci number (1-indexed)

online interpreter

Explanation

(1ä,1)        ; the matrix [[1,1],[1,0]]
       ^      ; to the power of
      #       ; the input
        M¡M   ; get the lower left element
        M¡    ; push the rows of the matrix reversed
          M   ; push all elements of the reversed lower row