For a singular matrix A = a i j 2 × 2 and the matrix B = 1 1 2 1 , if A B = B A , then 3 a 11 a 12 4 is equal to

Step-by-step solution

A = a 11 a 12 a 21 a 22 and A B = B A (given) i.e. a 11 a 12 a 21 a 22 1 1 2 1 = 1 1 2 1 a 11 a 12 a 21 a 22 ⇒ a 11 + 2 a 12 = a 11 + a 21   … i a 11 + a 12 = a 12 + a 22   … i i a 21 + 2 a 22 = 2 a 11 + a 21   … i i i and a 21 + a 22 = 2 a 12 + a 22   … i v From i i , a 11 = a 22 From i v , a 21 = 2 a 12 Since, A = 0 ⇒ a 11 a 22 - a 21 a 12 = 0 ⇒ a 11 2 = 2 a 12 2 ⇒ a 11 a 12 2 = 2 Hence, 3 a 11 a 12 4 = 12