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Show that the matrix B^T\ A B is symmetr...

Show that the matrix `B^T\ A B` is symmetric or skew-symmetric according as `A` is symmetric or skew-symmetric.

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If `A` be symmetric i.e., `A^{T}=A` then
`(B^{T} AB)^{T}=[B^{T}(AB)]^{T}=(AB)^{T}(B^{T})^{T} `
`=(B^{T} A^{T}) B=B^{T} A^{T} B=B^{T} AB`
Hence `B^{T} AB` is symmetric
If `A` is skew symmetric i.e., `A^{T}=-A` then
`(B^{T} A B)^{T}=[B^{T}(A B)]^{T}=(A B)^{T}(B^{T})^{T} `
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