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  • Let  be a <img alt="\mathrm{2 \times 2}" src="/latex-image/?%5Cmathrm%7B2%20%5Ctimes%202%

Let \mathrm{\text { A }} be a \mathrm{2 \times 2} matrix with det \mathrm{(A)=-1} and det \mathrm{((\mathrm{A}+\mathrm{I})(\operatorname{Adj}(\mathrm{A})+\mathrm{I}))=4}. Then the sum of the diagonal elements of \mathrm{\text { A }} can be :

Option: 1

-1


Option: 2

2


Option: 3

1


Option: 4

-\sqrt{2}


Answers (1)

best_answer

\mathrm{\text { Let } A=\left[\begin{array}{ll} a & b \\ c & d \end{array}\right], \text { ad }-b c=-1} \\

\mathrm{|A+I||a d j A+I|=4} \\

\mathrm{\Rightarrow a d-b c+a+d+1=2 \quad \text { or }-2} \\

\mathrm{a+d=2 \quad \text { or }-2}

Hence correct option is 2

Posted by

himanshu.meshram

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