\(A=2I+B \Rightarrow B = A-2I\)
\(\Rightarrow AB = A^2-2A=0\)
\(\Rightarrow A^2 = 2A \Rightarrow A^n = 2^{n-1} A,\,\forall n\in\mathbb{N}\)
\(\displaystyle\left(A+I\right)^8 = C^8_0 A^8 + C^8_1 A^7+\cdots+C^8_7A + C^8_8 I\)
\(\displaystyle= 2^7 C^8_0A + 2^6 C^8_1 A+\cdots + C^8_7 A + I\)
\(\displaystyle= \frac{1}{2}\left(2^8 C^8_0 + 2^7 C^8_1+\cdots 2C^8_7 +C^8_8 - 1\right) A +I\)
\(\displaystyle= \frac{1}{2}\left(3^8 - 1\right) A +I\)
\(\displaystyle= 3280 A+I\)
