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:

Question

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

MARKS App · Accepted Answer

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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