So, if we replace C by det(A), the equation from now becomes A * Adj(A) = (det(A))*IĪnd actually gives us the equation for A^(-1) if we manipulate it a little. Now observe that if we take the determinant of A, it is equal to the scalar C. Now, if you multiply A times Adj(A), you should see that it results in the identity matrix with the diagonal entries multiplied by some scalar that we'll call C, i.e. First we find the cofactor matrix, right? And then you take the transpose of the cofactor matrix. Say we want to find the inverse of a 3x3 matrix, using this theorem. So, you have the theorem that states: A^(-1) = Adj(A) * (1/det(A). I don't know how to represent a filled out matrix in text, so I'll do my best and try to generalize it in the abstract: I'm new to Reddit so I would like to apologize for any formatting mistakes that I make. I don't know of a strictly geometric interpretation, but I'd like to take a crack at explaining the reasoning behind it(adjoint of the cofactor matrix), by breaking down the theorem.
