Hi there again guys! I didnt really know what to call this thread, because my problem isnt actually to do with how to manipulate the elements of the matrix itself, but rather how to deal with the actual symbol for the matrix in equations. I'll start off with a fundamental thing, even though I'm not sure it makes sense. Suppose I have a matrix equation AB-1= C. Obviously the order matters unlike in regular algebra, so if I rearrange this for A, do i get A = BC or A = CB? how do I tell the order it needs to be in, generally? Now I'll go onto a specific example. I need to prove that (AT)-1 = (A-1)T. My text book makes sense until the last step. Here's what it says if I fill in some gaps: 1) Start with AA-1 = I = A-1A, where I is the identity matrix. 2) Transpose each term. So (AA-1)T = IT = (A-1A)T 3) Take AT out of the brackets: (A-1)TAT = AT(A-1)T. 4) Then it says "Clearly (A-1)T = (AT)-1"... I dont really get how that comes about, feels like it got plucked out of nowhere, unless im missing something stupid. I think mainly my problem is that im pretty new to this whole thing so I dont understand some basic operations. So if you guys know of some material online that maybe goes over this sort of thing, I'd love to check it out. Thanks guys!