Doing the computations by hand, find the determinant of the matrix A

In order to exploit the zeros, let’s expand along row 3. We then have

Notice that the second matrix here is singular since two rows are identical and thus it cannot row-reduce to an identity matrix. We now have

and now we expand on the first row of the first matrix:

= 2(−3) − (−3) − (−3) = 0