Discussion
In a rectangular standing arrangement of persons in four rows, each row having four persons. If jth person in the ith row is asked to move to the place of ith person of jth row for all i = 1, 2, 3, 4 and j = 1, 2, 3, 4, then how many persons have changed their original position ?
Answer: C
12 persons change their position.
The move sends the person at row i, place j to row j, place i, like transposing a 4 × 4 matrix. A person stays where they are only when i = j, that is, on the diagonal: 4 persons.
\[ 16 - 4 = 12 \]
Every off-diagonal person swaps with their mirror-image partner, so 12 move. 16 would mean nobody stays, and 4 counts only those who do not move.
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