Let \(A = [a_{ij}]\) be the square matrix of order 3 with \(a_{ij} = |i - j|\). Then \(|A|\) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4
Write down each element from the rule \(a_{ij} = |i - j|\); for example \(a_{13} = |1 - 3| = 2\) and every diagonal element is 0.
\(\displaystyle A = \begin{bmatrix}0 & 1 & 2\\ 1 & 0 & 1\\ 2 & 1 & 0\end{bmatrix}\)
Expanding along the first row:
\(|A| = 0(0 - 1) - 1(0 - 2) + 2(1 - 0)\)
\(|A| = 0 + 2 + 2 = 4\)