JEE Advanced 2023 Paper 2 Solutions

|R|=−5|

a	b
c	d

|
|R| can be zero in following cases:
(i) Two of a,b,c,d are zeroes which can be ( a and b),(b and d), ( d and c ) or ( c and a)
→4×72 ways =196
(ii) Any three of a,b,c,d are zeroes
→‌4C3×7=28
(iii) All four of a,b,c,d are zeroes
→1
(iv) All four of a,b,c,d are non-zero but same number
→7
(v) When two are alike and 2 other are alike (non-zero)
→7C2×2×2=84
Number of invertible matrices =84−196−28−1−7−84=3780