Match the items of List- I with the items of List- II and choose the correct option List- I List- II ( A ) If A is a non-singular matrix of order 3 and | A | = a , then adj A - 1 - 1 = ( I ) null matrix ( B ) A is a non-singular matrix of order 3 and B is any matrix of order 3 such that A B = O , then B is ( II ) a 2 ( C ) 1 x x 2 cos ( a - b ) y cos α y cos ( a + b ) y sin ( a - b ) y sin α y sin ( a + b )

Step-by-step solution

( A ) The non-singular matrix of order 3 , | A | = a , adj A - 1 - 1 ∣ = 1 adj A - 1 = 1   A - 1 2 | adj A | = | A | 2 , if order of A is 3 = 1 1 |   A | 2 = | A | 2 = a 2 B It is given that for non-singular matrix A of order B ,   A B = 0 | A B | = 0 ⇒ A B   = 0 ⇒ B = 0 ∵ | A | ≠ 0 And matrix B should be null matrix. C Δ = 1 x x 2 cos ( a - b ) y cos a y cos ( a + b ) y sin ( a - b ) y sin a y sin ( a + b ) y By simplifying the above equation, we get sin ( b y