Consider the matrix A=(01−23)A = \begin{pmatrix} 0 & 1 \\ -2 & 3 \end{pmatrix}A=(0−213). What is A10A^{10}A10?
210I−(210−1)A2^{10}I - (2^{10}-1)A210I−(210−1)A
(210−1)A−I(2^{10}-1)A - I(210−1)A−I
210A−I2^{10}A - I210A−I
A2+10IA^2 + 10IA2+10I