Problem 4. (6+ 4 points) (i) Use Gauss-Jordan elimination to compute the inverse and determinant of the following matrix. B 2 -1 0 0 -1 0 0 2 -1 0 2

-1 -1 0 -1 2 (ii) Suppose that A is a 4 x 4 matrix such that adj(A) = B, i.e. the matrix in the previous part of the question. Find A. Hint: You may need to use certain mathematical statements stated in tutorial problem set 4. (In fact, this demonstrates that knowing the adjoint matrix of an invertible matrix allows you to recover the original matrix back.)