JEE Main202226 Jul 2022Morning ShiftMathematicsMatricesActual

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:

Options

A- 1
B2
C1
D- 2

Correct answer

B. 2

Step-by-step solution

Let A = a b c d , so a d j A = a - b - c d Now given A = - 1 So, a d - b c = - 1 Now A + I adj A + I = 4 ⇒ A a d j A + a d j A + A + I = 4 ⇒ A I + a d j A + A + I = 4 ⇒ - I + a d j A + A + I = 4 ⇒ a d j A + A = 4 ⇒ a + d 0 0 a + d = 4 ⇒ a + d 2 = 4 So, a + d = 2 or - 2

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