Mathematics

Problem

Let

A = [a_{ij}]

and

B = [b_{ij}]

be two

3 \times 3

real matrices such that

b_{ij} = (3)^{(i+j-2)}a_{ji}

, where

i, j = 1, 2, 3

. If the determinant of

B

is 81, then the determinant of

A

is [JEE (Main)-2020] (1)

1/9

(2)

1/81

(3) 3 (4)

1/3