my father enjoys the books written by Akasha.
written是过去分词做后置定语,修饰books.
句子也可以写为
my father enjoys the books （which/that were) written by Akasha.括号里的可以省略,因为（which/that were) written by Akasha 是定语从句,起修饰作用,而不是一个单独的主句.
而 keys are used for opening the door.钥匙是用来开门的.这是一个独立的句子,如果省略了be动词（are）的话,句子就不对了.
被动语态 be used for
举个例子
This key is used for opening my room.is不能省略
I lost the key (which/ that is) used for opening my room.括号的能省略.
缘由如上.