Question 191470
Since we have a upper triangular matrix, this means that the determinant is simply the product of all of the diagonal entries. So 


det(A)=(1)(1)(-1)=-1



So the determinant of A is -1



Since the determinant is NOT equal to zero, this means that the inverse of A exists. To find the inverse of A, you have many options, but the best option (in my opinion) is to row reduce the augmented matrix {{{AI}}}. So append the 3x3 matrix {{{(matrix(3,3,1,0,0,0,1,0,0,0,1))}}} to {{{A=(matrix(3,3,1,-2,-1,0,1,2,0,0,-1))}}} to get 





{{{(matrix(3,6,1,-2,-1,1,0,0,0,1,2,0,1,0,0,0,-1,0,0,1))}}}



From there, just row reduce the 3x6 matrix to find {{{A^(-1)}}}. Let me know if you need help with the row reduction.



Note: you should get the answer: {{{A^(-1)=(matrix(3,3,1,2,3,0,1,2,0,0,-1))}}}