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

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 : (A) -1 (B) 2 (C) 1 (D) -√2

Tardigrade Admin · Accepted Answer

Let A=[ a b c d ] ; ad - bc =-1 | A + I || operatornameadj A + I |=4 ⇒ ad - bc + a + d +1=2 text or -2 a + d =2 text or -2

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

$- 1$

2

1

$- 2$

Let $A = [a c b d]; a d - b c = - 1$
$∣ A + I ∣∣ adj A + I ∣ = 4$
$\Rightarrow a d - b c + a + d + 1 = 2 or - 2$
$a + d = 2 or - 2$

Q. Let A be a 2×2 matrix with det (A)=−1 and det((A+I)(Adj(A)+I))=4. Then the sum of the diagonal elements of A can be :

−1

2

1

−2​

Let A=[ac​bd​];ad−bc=−1 ∣A+I∣∣adjA+I∣=4 ⇒ad−bc+a+d+1=2 or −2 a+d=2 or −2

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

$- 1$

$- 2$

Let $A = [a c b d]; a d - b c = - 1$
$∣ A + I ∣∣ adj A + I ∣ = 4$
$\Rightarrow a d - b c + a + d + 1 = 2 or - 2$
$a + d = 2 or - 2$