Let A be a 2 × 2 matrix with real entries such that A ' = α A + 1 , where α ∈ ℝ - - 1 , 1 ., If det A 2 - A = 4 , the sum of all possible values of α is equal to

Step-by-step solution

Given, A be a 2 × 2 matrix with real entries such that A ' = α A + 1 , Now let A = a b c d Now putting the value in A ' = α A + I we get, ⇒ a c b d = α a + 1 α b α c α d + 1 Now equating both side we get, a = α a + 1 ⇒ a = 1 1 - α   . . . . . . . . . i b = α c   . . . .   i i and c = α b   . . . . . . . . i i i Now from equation i i   &   i i i we get, c = 0 or α = ± 1 (not possible as mentioned in