Let A = a11 a12 a13
a21 a22 a23
a11 a12 a13

where ai j ∈ R for each 1 ≤ i, j ≤ 3.

Which of the following is/are true?

A. det (A) = 0

B. det(A) depends only on the values of the entries ai j , 1 ≤ i, j ≤ 3.

1. Only A 2. Only B 3. Both A and B 4. Neither A nor B.

Question

Let A =  a11 a12 a13
              a21 a22 a23
              a11 a12 a13 

where ai j ∈ R for each 1 ≤ i, j ≤ 3. 

Which of the following is/are true? 

A. det (A) = 0

B. det(A) depends only on the values of the entries ai j , 1 ≤ i, j ≤ 3. 

1. Only A     2. Only B     3. Both A and B     4. Neither A nor B.

unklerhaukus · Answer

notice how one row is a repeat,
$\rightarrow$the rows are not linearly independent 
$\rightarrow$the determinant is zero

unklerhaukus · Answer

also notice how A and B are contradict each other

anonymous · Answer

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therefore answer is 1.onlyA