Q70 / 155 · WBJEE 2023 · Mathematics
Let \(A=\left(\begin{array}{ccc}2 & 0 & 3 \\ 4 & 7 & 11 \\ 5 & 4 & 8\end{array}\right)\). Then
- Correct answerA\(\operatorname{det} A\) is divisible by 11
- B\(\operatorname{det} A\) is not divisible by 11
- C\(\operatorname{det} A=0\)
- DA is orthogonal matrix
Solution
\(\begin{aligned}
& \text {Hint: } \operatorname{det}(A)=2(56-44)+0+3(16-35) \\
& =24-57 \\
& =-33 \text { which is divisible by } 11
\end{aligned}\)
Hence, the correct answer is option: 'A'.