When is a 3 x 3 Matrix invertible?
You’ve done half the work. The matrix is invertible because the determinant in nonzero. Now, to find the inverse, just take the reciprocal of your determinant (so -0.1) and multiply it by the adjoint (or adjugate) of the matrix. To do that, go through the steps in the link below. Basically, for each one of the 9 elements in your original matrix, form a 2 x 2 matrix by eliminating the row and column of that element. Now take the determinants. Replace the original members of your 3 x 3 matrix by the corresponding determinants of the corresponding 2 x 2 matrices. Then, if the number and the row number of an element add up to an odd number, change the sign of that number. Leave the others alone. This is your adjoint. Multiply that, as I said above, by -0.1, and you have your inverse.
