JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) be a \(2 \times 2\) matrix with \(\operatorname{det}(A)=-1\) and det \((( A + I )(\operatorname{Adj}( A )+ I ))=4\). Then the sum of the diagonal elements of \(A\) can be.
- A \(-1\)
- B \(2\)
- C \(1\)
- D \(-\sqrt{2}\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
Let \(A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] ; a d-b c=-1\) \(| A + I ||\operatorname{adj} A + I |=4\) \(\Rightarrow ad - bc + a + d +1=2 \text { or }-2\) \(a + d =2 \text { or }-2\)
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