Given two matrices A and B which you can multiply together, does (A B)^T = A^T B^T or B^T A^T?

The correct answer is ( A B )^ T = A ^ T B ^ T . \n \n To understand this , we need to know what matrix multi plication means . When we multip ly two matrices A and B , we get a new matrix C , where C [ i , j ] = sum ( A [ i , k ] * B [ k , j ]) for all i and j . \n \n The trans pose of a matrix A , denoted by A ^ T , is a new matrix where A ^ T [ i , j ] = A [ j , i ] for all i and j . \n \n Now , when we multip ly two matrices A and B , we can think of it as multip lying A by B ' s trans pose , where B ' is the matrix obtained by taking the trans pose of B . So , ( A B )^ T = A ^ T B ' = A ^ T ( B ^ T ). \n \n There fore , the correct answer is ( A B )^ T = A ^ T B ^ T . </s>