How are you supposed to find the fastest way to calculate A2

How are you supposed to find the fastest way to calculate A^(2)x?

Suppose A is a 4 times 4 matrix A = (a_11 a_21 a_31 a_41 a_12 a_22 a_32 a_42 a_13 a_23 a_33 1_43 a_14 a_24 a_34 a44) with entries a_ij epsilon R, 1 lessthanorequalto i, j lessthanorequalto 4. If x epsilon R^4, what is the fastest way top calculate A^2x?

Solution

If exponent of A is bigger then converting A into diagonal matrix and then calculating power of A will be faster way.

But since here exponent of A is just 2 so usual multiplication will be easy.

That is calculate A^2 by multiplying A with A.

Then multiply result A^2 by matrix x to find A^2x