If A=(2003)A = \begin{pmatrix} 2 & 0 \\ 0 & 3 \end{pmatrix}A=(2003) is diagonal, what is A4A^4A4 (i.e., AAAAAAAAAAAA)?
(160081)\begin{pmatrix} 16 & 0 \\ 0 & 81 \end{pmatrix}(160081)
(80027)\begin{pmatrix} 8 & 0 \\ 0 & 27 \end{pmatrix}(80027)
(4009)\begin{pmatrix} 4 & 0 \\ 0 & 9 \end{pmatrix}(4009)
(60012)\begin{pmatrix} 6 & 0 \\ 0 & 12 \end{pmatrix}(60012)