2. The determinant of matrix \( \mathbf{A} \) is nonzero if and only if the reduced row echelon form of \( \mathbf{A} \) is the identity matrix.
2. The determinant of matrix \( \mathbf{A} \) is nonzero if and only if the reduced row echelon form of \( \mathbf{A} \) is the identity matrix.