Let \(A\) be a \(3 \times 3\) matrix such that \(\operatorname{adj}(A)=\left[\begin{array}{ccc}25 & 0 & 100 \\ 0 & 4 & 3 \\ 0 & 100 & 100\end{array}\right]\), then determinant of \(A\) is
Show Hint
- 25
- 50
- 100
- 1000
The Correct Option is B
Solution and Explanation
Expand along the first column: \(|\operatorname{adj}A| = 25\,(4\cdot 100-3\cdot 100) = 25\cdot 100 = 2500\).
So \(|A|^2=2500\), giving \(|A|=50\) (taking the positive value, the only one among the options).
Answer: (2) 50
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