Let `A*B=A^(T)B^(-1)` where `A^(T)` represents transpose of matrix `A` and `B^(-1)` represents inverse of square matrix `B`. This operation is defined when the number of rows of `A` is equal to the number of rows of `B`. Matrix `A` is said to be orthogonal if `A^(-1)=A^(T)`
If `A*B` is defined then which of the following operations are always define?

Options

A. `(A*B)^(-1)=B*A` if `A` is symmetric matrix
B. `(A*B)^(T)=A*B^(-1)` if `B` is orthogonal matrix
C. `(A*B)^(T)=B^(-1)*A` if `A` is orthogonal matrix
D. `(A*B)^(-1)=B*A^(-1)` if `B` is symmetric matrix

Answer

A, C, D

Explanation

NA