# Raising The Stakes

Algebra Level 4

Let $$A = \begin{bmatrix}2 & 1 \\-1 & 4 \end{bmatrix}$$ and $$B = A^{2016}$$, then find the remainder when $$b_{22}$$ is divided by 7.

 Clarification: $$b_{ij}$$ denote element of the matrix $$B$$ in the $$i^\text{th}$$ row and $$j^\text{th}$$ column.

×