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Question: Answered & Verified by Expert
Let \(A=\left(\begin{array}{ccc}2 & 0 & 3 \\ 4 & 7 & 11 \\ 5 & 4 & 8\end{array}\right)\). Then
MathematicsDeterminantsWBJEEWBJEE 2023
Options:
  • A \(\operatorname{det} A\) is divisible by 11
  • B \(\operatorname{det} A\) is not divisible by 11
  • C \(\operatorname{det} A=0\)
  • D A is orthogonal matrix
Solution:
1411 Upvotes Verified Answer
The correct answer is: \(\operatorname{det} A\) is divisible by 11
\(\begin{aligned}
& \text {Hint: } \operatorname{det}(A)=2(56-44)+0+3(16-35) \\
& =24-57 \\
& =-33 \text { which is divisible by } 11
\end{aligned}\)

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