UPSC NDA I 2021 Mathematics Solved Paper

Concept
If all the elements of a row or column are zeroes, then the value of the determinant is zero. To evaluate the determinant row or column operation is done.
Calculation:
The determinant can be written as,
[

2(1+1)	2(1+2)	2(1+3)
2(2+1)	2(2+2)	2(2+3)
2(3+1)	2(3+2)	2(3+3)

]
‌‌=2×[

1+1	1+2	1+3
2+1	2+2	2+3
2+1	3+2	3+3

]
R3→R3−R1‌ and ‌R2→R2−R1
‌‌=2×[

1+1	1+2	1+3
1	1	1
2	2	2

]
R3→R3−2R2
‌‌=2×[

1+1	1+2	1+3
1	1	1
0	0	0

]
‌‌=0
So, the value of the determinant is 0