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 trans pose of a matrix is obtained by inter ch anging its rows and columns . Therefore , the trans pose of matrix A is A ^ T and the trans pose of matrix B is B ^ T . \n \n Now , when you multiply two matrices A and B , the result is a new matrix C , where each element C ( i , j ) is the dot product of the corresponding elements of A and B . Therefore , the trans pose of the product matrix C is C ^ T . \n \n So , we have : \n \n C = A B \n \n C ^ T = A ^ T B ^ T \n \n There fore , ( A B )^ T = A ^ T B ^ T . </s>