Prove that A=B if and only if A's transpose = A's transpose .
if and only if 證明題，證明過程有和技巧?
更新1:
if and only if 證明題，證明過程什麼技巧?
更新2:
For example: Let A and Bbe symmetric matrices of the same size. Prove that the product AB is symmetric if and and only if AB=BA. (a)Let AB be symmetric. Then AB=(AB)^t =(B^t)(A^t) =BA (b)Let AB=BA. Then (AB)^t=(BA)^t =(A^t)(B^t) =AB
更新3:
1. A = B => A^T = B^T 2. A^T = B^T => A = B Why? A = B => A^T = B^T 你可以直接得知A^T = B^T， 過程中不需要再有其他證明?