This question was previously asked in

Airforce Group X 4 November 2020 Memory Based Paper

Option 1 : 0

Group X 2021 Full Mock Test

80603

70 Questions
70 Marks
60 Mins

__ CONCEPT__:

**Properties of Determinant of a Matrix**:

- If each entry in any row or column of a determinant is 0, then the value of the determinant is zero.
- For any square matrix say A, |A| = |A
^{T}|. - If we interchange any two rows (columns) of a matrix, then the determinant is multiplied by -1.
- If any two rows (columns) of a matrix are same then the value of the determinant is zero.

__ CALCULATION__:

Here, we have to find the value of \(\left| {\begin{array}{*{20}{c}} 3&2&1\\ 3&2&1\\ 1&0&1 \end{array}} \right|\)

As we can see that the first and the second row of the given matrix are equal.

We know that, if any two rows (columns) of a matrix are same then the value of the determinant is zero.

So, \(\left| {\begin{array}{*{20}{c}} 3&2&1\\ 3&2&1\\ 1&0&1 \end{array}} \right| = 0\)

Hence, **option A** is the correct answer.