If A=[2003]A = \begin{bmatrix} 2 & 0 \\ 0 & 3 \end{bmatrix}A=[2003], compute A10A^{10}A10 using diagonalization.
[10240059049]\begin{bmatrix} 1024 & 0 \\ 0 & 59049 \end{bmatrix}[10240059049]
[2003]\begin{bmatrix} 2 & 0 \\ 0 & 3 \end{bmatrix}[2003]
[200030]\begin{bmatrix} 20 & 0 \\ 0 & 30 \end{bmatrix}[200030]
[21000310]\begin{bmatrix} 2^{10} & 0 \\ 0 & 3^{10} \end{bmatrix}[21000310]