If A is a 2 × 2 matrix such that A 1 - 1 = - 1 2 and A 2 1 - 1 = 1 0 , then trace of A is (where, the trace of the matrix is the sum of all principal diagonal elements of the matrix)

Step-by-step solution

Let, A = a b c d A 1 - 1 = - 1 2 ⇒ a b c d 1 - 1 = - 1 2 On solving, we get, a - b = - 1 , c - d = 2 Also, A 2 1 - 1 = A A 1 - 1 = A - 1 2 = 1 0 This gives, - a + 2 b = 1 , - c + 2 d = 0 ⇒ b = 0 , a = - 1 , d = 2 , c = 4