Let a ∈ R and A be a matrix of order 3 × 3 such that det(A) = –4 and A + I = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ 2 1 a 0 1 2 1 a 1 , where I is the identity matrix of order 3 × 3. If det ((a + 1) adj((a – 1)A)) is 2 m 3 n , m, n ∈ {0, 1, 2, …, 20}, then m + n is equal to :

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Let a ∈ R and A be a matrix of order 3 × 3 such that det(A) = –4 and A + I = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ 2 1 a 0 1 2 1 a 1 , where I is the identity matrix of order 3 × 3. If det ((a + 1) adj((a – 1)A)) is 2 m 3 n , m, n ∈ {0, 1, 2, …, 20}, then m + n is equal to :

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