You can also use the SVD decomposition instead of LU, which provides a condition number to get an idea how ill-conditioned the matrix is.
You're right, Inverse and Determinant (and also ConditionNumber) are all also available at the matrix, but they do not cache the decomposition. If your matrix is large you may want to reuse it (by using it explicitly as in my example above).
You're right, Inverse and Determinant (and also ConditionNumber) are all also available at the matrix, but they do not cache the decomposition. If your matrix is large you may want to reuse it (by using it explicitly as in my example above).