WBJEE · Maths · Determinants
Let \(A=\left(\begin{array}{ccc}2 & 0 & 3 \\ 4 & 7 & 11 \\ 5 & 4 & 8\end{array}\right)\). Then
- 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
Answer & Solution
Correct Answer
(A) \(\operatorname{det} A\) is divisible by 11
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Hint: } \operatorname{det}(A)=2(56-44)+0+3(16-35) \\ & =24-57 \\ & =-33 \text { which is divisible by } 11 \end{aligned}\)
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