If A 1 , A 2 , A 3 … … . A 20 are 20 skew-symmetric matrices of same order and B = ∑ r = 1 20 2 r A r 2 r + 1 , then the sum of the principal diagonal elements of matrix B is equal to

Step-by-step solution

A 1 T = - A 1 , A 2 T = - A 2 , … . . , A 20 T = - A 20 B = ∑ r = 1 20 2 r A r 2 r + 1 B T = ∑ r = 1 20 2 r A r 2 r + 1 T = ∑ r = 1 20 2 r A r T 2 r + 1 = ∑ r = 1 20 2 r - A r 2 r + 1 = - ∑ r = 1 20 2 r A r 2 r + 1 = - B ⇒ B is skew-symmetric Hence, the sum of principal diagonal elements of B = 0