If `A_1, A_2, , A_(2n-1)a r en` skew-symmetric matrices of same order, then `B=sum_(r=1)^n(2r-1)(A^(2r-1))^(2r-1)` will be symmetric skew-symmetric neither symmetric nor skew-symmetric data not adequate

Options

A. symmetric
B. skew-symmetric
C. neither symmetric nor skew-symmetric
D. data not adequate

Answer

B

Explanation

`B=A_(1) +3 A_(3)^(3)+...+ (2n-1) (A_(2n-1))^(2n-1)`
`B^(T)=-[A_(1)+3A_(3)^(3)+...+ (2n-1) (A_(2r-1))^(2r-1)]`
`=-B`
Hence, B is skew-symmetric.