Let A = a b c d and B = α β ≠ 0 0 such that A B = B and a + d =2021, then the value of a d - b c is equal to ______ .

Step-by-step solution

Given A = a b c d ,   B = α β And, A B = B ⇒ ( A - I ) B = O ⇒ ( A - I ) B = 0 ⇒ ( A - I ) × B = 0 ⇒ | A - I | = 0 , since B ≠ 0 ⇒ ( a - 1 ) b c ( d - 1 ) = 0 ⇒ a - 1 d - 1 - b c = 0 ⇒ a d - a - d + 1 - b c = 0 ⇒ a d - b c = a + d - 1 ⇒ a d - b c = 2021 - 1 = 2020 .