Let S = - 1 a 0 b ; a , b ∈ 1 , 2 , 3 , … 100 and let T n = A ∈ S : A n n + 1 = I . Then the number of elements in ∩ n = 1 100 T n is _____.

Step-by-step solution

Given, A = - 1 a 0 b A 2 = - 1 a 0 b - 1 a 0 b = 1 - a + a b 0 b 2 ∴ T n = A ∈ S ; A n a + 1 = I ∴     b must be equal to 1 ∴ In this case A 2 will become identity matrix and a can take any value from 1 to 100 ∴ Total number of common element will be 100 .