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.

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