| |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