If \(A=\left(\begin{array}{ll}3 & -2 \\ 2 & -1\end{array}\right)\), then A²⁰ equals

Calculation: 

Given 

\(A=\left(\begin{array}{ll}3 & -2 \\ 2 & -1\end{array}\right)\)

\(A^2=\left(\begin{array}{ll}5 & -4 \\ 4 & -3\end{array}\right)\)

\(A^4=\left(\begin{array}{ll}9 & -8\\ 8 & -7\end{array}\right)\)

\(A^8=\left(\begin{array}{ll}17 & -16\\ 16 & 15\end{array}\right)\)

\(A^{16}=\left(\begin{array}{ll}33 & -32\\ 32 & 31\end{array}\right)\)

and 

A ²⁰ = \(\left(\begin{array}{ll} 41 & -40 \\ 40 & -39 \end{array}\right)\)

Hence option (2) is correct