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WBJEE · Maths · Matrices

If for a matrix \(A,|A|=6\) and adj \(A=\left[\begin{array}{ccc}1 & -2, & 4 \\ 4 & 1 & 1 \\ -1 & k & 0\end{array}\right]\), then \(k\) is equal to

  1. A \(-1\)
  2. B \(1\)
  3. C \(2\)
  4. D \(0\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(2\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { } A \cdot(\operatorname{adj} A)=|A| I \\ & \Rightarrow|A||\operatorname{adj} A|=|A|^3 \Rightarrow|\operatorname{adj} A|=|A|^2 \\ & -1((-2-4)-K(1-16)=36 \Rightarrow 6-K+16 K=36 \\ & \Rightarrow 15 K=30 \Rightarrow K=2\end{aligned}\)