1. Tardigrade
  2. Question
  3. Mathematics
  4. Let A be a 2 × 2 matrix with det ( A )=-1 and operatornamedet(( A + I )( operatornameAdj( A )+ I ))=4. Then the sum of the diagonal elements of A can be :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

JEE MainJEE Main 2022Determinants

Solution:

Let $A=\begin{bmatrix} a & b \\ c & d \end{bmatrix} ; ad - bc =-1$
$ | A + I ||\operatorname{adj} A + I |=4$
$ \Rightarrow ad - bc + a + d +1=2 \text { or }-2$
$ a + d =2 \text { or }-2$