Let M denote the set of all real matrices of order 3 × 3 and let S = –3, –2, –1, 1, 2 . Let S_1 = A = [a_ ij...

Question

Let M denote the set of all real matrices of order 3 × 3 and let S = –3, –2, –1, 1, 2 . Let S_1 = A = [a_ ij ] M : A = A^T and a_ ij S, i, j S_2 = A = [a_ ij ] M : A = -A^T and a_ ij S, i, j S_3 = A = [a_ ij ] M : a_ 11 + a_ 22 + a_ 33 = 0 and a_ ij S, i,j If n(S_1 S_2 S_3) = 125 , then equals.

Accepted Answer

1613

JEE Main 2025 Mathematics question

Solution