Let and be the identity matrix of order 3

MATHEMATICS · Single correct · CBSE · Mathematics · Matrices · Matrices

Problem

Let

P = \begin{bmatrix} 1 & 0 & 0 \\ 4 & 1 & 0 \\ 16 & 4 & 1 \end{bmatrix}

and

I

be the identity matrix of order 3. If

Q = [q_{ij}]

is a matrix such that

P^{50} - Q = I

, then the sum of digits in

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

= (A) 5 (B) 4 (C) 6 (D) 10