Let S = A = pmatrix 0 & 1 & c 1 & a & d 1 & b & e pmatrix : a, b, c, d, e 0, 1 and |A| -1, 1 , where |A| denotes the determinant of A. Then the number of elements in S is _____.

JEE Advanced 2024 Mathematics question

Let , where denotes the determinant of . Then the number of elements in is .

Answer: 16

Expanding along the first row: . If : need , i.e. or , with free: . If : need

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Question ID VK-034173