Question

If \(A = [a_{ij}]\) be a 3 x 3 matrix, where \(a_{ij} = i - 3j\), then which of the following is false?

(A) \(a_{11} < 0\)

(B) \(a_{12} + a_{21} = - 6\)

(C) \(a_{13} > a_{31}\)

(D) \(a_{31} = 0\)

Answer 1

Correct option is (C) \(a_{13} > a_{31}\) 

(A) \(a_{11} = 1 - 3 = -1 < 0\)  (True)

(B) \(a_{12} + a_{21} = 1 - 3 \times 2 + 2-3\times 1 = -6\)  (True)

(C) \(a_{13} > a_{31} \to 1 - 3\times 3 > 3 - 3\times 1 \to -8>0\)  (False)

(D) \(a_{31} = 3 - 3 \times 1 = 0\)  (True)