另一种计算矩阵在R中的行列式的方法

So it is a mathematical fact that if the determinant of a matrix is equal to zero, then the matrix must be singular (not invertible). Now, the problem I am running into is that when I calculate the determinant of my matrix it is equal to zero, however, when I calculate the inverse it exist. I think it has to do with the way R calculates determinants that the two are not agreeing. Here is the code that I am trying (I wont print the results of solve because the matrix is 100 x 100).So it is a mathematical fact that if the determ