Matrices & Determinants · Powers of a matrix

Let

A = \begin{bmatrix} 1 & 0 & 0\\ 3 & 1 & 0\\ 9 & 3 & 1\end{bmatrix} \quad\text{and}\quad B = [b_{ij}],\ 1 \le i, j \le 3.

B = A^{99} - I

, then the value of

\dfrac{b_{31} - b_{21}}{b_{32}}

is:

We corrected a printing error in the original paper

Source printed “ $B = [b_{ij}]$ , $l \le i, j \le 3$ ” (letter l for the digit 1).

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