26. (5%) Let \( \mathbf{U} \) be an \( n \times n \) unit upper triangular matrix. It is known that \( \mathbf{U} \) is nonsingular. Now, \( \mathbf{U}^{-1} \) is derived by transforming \( [\mathbf{U} \mathbf{I}] \) into \( [\mathbf{I} \mathbf{U}^{-1}] \) via row operations. Use the above derivation method to prove that \( \mathbf{U}^{-1} \) is also unit upper triangular.