Select and write the most appropriate answer from the given alternatives in each of the following :
If `A = {:((2,-3),(4,1)):}`, then adjoint of matrix A is

Options

A. `[(1,3),(-4,2)]`
B. `[(1,-3),(-4,2)]`
C. `[(1,3),(4,-2)]`
D. `[(-1,-3),(-4,2)]`

Answer

A

Explanation

Given, `A = [(2,-3),(4,1)]`
Cofactors of the given matrix are :
` m_(11) = 1`
` rArr A_(11) = (-1)^(2) . (1) = 1`
` m_(12) = 4`
` rArr A_(12) = (-1)^(3) . (4) = - 4`
` m_(21) = - 3`
` rArr A_(21) = (-1)^(3) . (-3) = 3`
` m_(22) = 2`
` rArr A_(22) = (-1)^(4).(2) = 2`
` :. ` Matrix of cofactors = `[(1,-4),(3,2)]`
` :. " adj. A" = [(1,-4),(3,2)]^(T) = [(1,3),(-4,2)]`
Hence, the correct answer from the given alternatives is (a) .