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**Matrices, Transposes, and Inverses. --- Help?**

Say, you have Matrix A, Y, and a matrix of coefficients C not neccissarily square, and A * C = Y. To solve this, i would think to multiply both sides by the inverse of A, but since it's not necessarily square that won't work. I've seen a solution that I am having some questions about. It multiplies both sides by ATranspose, then it multiplies both sides by (A * ATranspose) ^-1. I think i understand that multiplication by ATranspose, so as to get it into a square matrix. Then, i guess i understand the multiplication by the inverse of it, but i think i read somewhere that it is particularly easier to take the inverse of A * Atranspose. I need the simplest method possible, because i have to code a program to solve this equation for me, in C++. I can figure out the code, if i can find a step by step process to finding the inverse, but I am really confused regarding taking inverses in general, and if it's easier if you multiply it by the transpose first.

I'd appreciate any help, and, if possible, i need this kinda soon, but even if the deadline passes, i still want to understand, for myself how it's done.