Let be such that

MATHEMATICS · Single correct · CBSE · Mathematics · Determinants · Determinants

Problem

Let

A=[a_{ij}]_{3\times3}

be such that

a_{ij}=\begin{cases}3, & \text{when } i=j\\0, & i\ne j\end{cases}

. Then

\left\{\frac{\det(\operatorname{adj}(\operatorname{adj} A))}{5}\right\}

equals, where

\{\cdot\}

denotes the fractional-part function: (a)

\frac{2}{5}

(b)

\frac{1}{5}

(c)

\frac{2}{3}

(d)

\frac{1}{3}