I have been reviewing linear algebra for my FE exam, and I was thinking about cofactors. What are these strange things? It totally mystifies me that you can make a cofactor matrix from a matrix A (where the does alternating +/- come from??), transpose it, find the determinant (I still don't understand what this thing is, just something I know how to calculate), then divide that determinant by the adjoint to find the inverse of the original matrix A. How in the heck do all these things relate to each other? What is the underlying meaning here other than to say that you can calculate the matrix inverse. It looks like magic to me!!