Determinants · Question 33

Let A = [aij] = bmatrix 5 128 & 4 5 \ 5 8 & 4 25 bmatrix. If Aij is the cofactor of aij, Cij = k=12 aikAjk, 1 i, j 2, and C = [Cij], then 8|C| is equal to :

1. 288
2. 262
3. 222
4. 242

Answer

(4) 242

Solution

k=12 aikAjk = |A| if i = j and 0 if i j (expansion by own / other row's cofactors)

C = A(adj A) = |A| I

|C| = |A|2

|A| = 5 128 4 25 - 4 5 5 8

= 7 5 2 2 5 - 12 2 5 3 5 2

= 7 - 32 = 112

8|C| = 8 1214 = 242

Answer: (4)