Mathematics

Problem

Let

P = \begin{bmatrix} 1 & 0 & 0 \\ 3 & 1 & 0 \\ 9 & 3 & 1 \end{bmatrix}

and

Q = [q_{ij}]

be two

3 \times 3

matrices such that

Q - P^5 = I_3

. Then

\frac{q_{21} + q_{31}}{q_{32}}

is equal to (1) 10 (2) 135 (3) 9 (4) 15