1. The problem statement, all variables and given/known data Write the general element in terms of aij and bij for (AB)^T [AB transposed]. 2. Relevant equations (AB)^T = B^T*A^T; A=[aij]mxn; B=[bij]nxp 3. The attempt at a solution n AB= [sigma aik*bkj]mxp. Let this be equal to [xij]mxp k=1 n (AB)^T=[[sigma aik*bkj]mxp]^T k=1 =[xji]pxm n =[sigma aki*bjk]mxp k=1 n so the general element xji=[sigma aki*bjk] k=1 My teacher says this is wrong. Where did I go wrong? ------------------------ Alternate way I used to "check" my wrong answer: n (AB)^T=B^T*A^T=[bji]pxn[aji]nxm=[sigma bjk*aki]pxm=[sigma aki*bjk]pxm k=1 We are using an differential equations/linear algebra textbook for engineers. It never discusses element-by-element proofs, and it leaves out many important differential equations topics, such as exact equations. I have a real diff eq book that my neighbor lent me, but I have to teach myself these types of problems through Wikipedia.