I have a question about the time complexity of finding the nth Fibonacci number using matrices.
I know that you can find $F_n$ from:
$ \begin{pmatrix} 1 & 1\\ 1 & 0\\ \end{pmatrix}^n = \begin{pmatrix} F_{n+1} & F_n\\ F_n & F_{n-1}\\ \end{pmatrix} $
From above, $F_n$ is the entry in row 1, column 2 of the matrix. I have read in an online source that raising the Fibonacci Q-matrix to the power of n takes O(n) time. I am not sure why this is the case. Is matrix multiplication an operation that can be done in constant time on computers? That is the only reason I can see the above operation taking O(n) time (since you would have to do n-1 multiplications to raise the Q-matrix to the power of n). Any insights are appreciated.