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JEE Advanced 2012Paper 2
Exam
JEE Advanced
Year
2012
Paper
Paper 2
Subject
Mathematics
Chapter
Matrices

JEE Advanced 2012 · Paper 2 · Mathematics · Matrices

If the adjoint of a 3 × 3 matrix P is [ array lll 1 & 4 & 4 2 & 1 &...

If the adjoint of a 3×33 \times 3 matrix PP is \left[144217113\begin{array}{lll}1 & 4 & 4 \\ 2 & 1 & 7 \\ 1 & 1 & 3\end{array}\right], then the possible value(s) of the determinant of PP is (are)

Options

  1. A−2-2
  2. B−1-1
  3. C1
  4. D2

Correct answer

A. −2-2

Step-by-step solution

We know for a third order matrix PP, ∣Adj⁡P∣=∣P∣2|\operatorname{Adj} P|=|P|^{2} Where ∣Adj⁡P∣=1(3−7)−4(6−7)+4(2−1)=4∴∣P∣2=4P∣P∣=2 or −2\begin{aligned} &|\operatorname{Adj} P|=1(3-7)-4(6-7)+4(2-1)=4 \\ \therefore \quad &|P|^{2}=4 \mathrm{P}|P|=2 \text{ or }-2 \end{aligned}
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