Fibonacci using Matrix Representation. Fibonacci using matrix representation is of the form :
Fibonacci Matrix. This claims to be of O(log n).However, isn't computing matrix multiplication of order O(n^3) or using Strassen's algorithm O(n^2.81)? How can this be solved in O(log n)?

Matrix multiplication is $O(n^{2.81})$, where $n$ is the size of the matrix.  The matrix size is constant here ($n = 2$).  So each matrix multiplication takes constant time.
If we want $f_k$, there are $\log k$ matrix multiplications needed.  Each takes constant time, so the total time is $O(\log k)$.
