First, make sure that your matrix is “square”. That means, it must be 2×2 or 3×3 or 4×4….
Then, press the Math Templates button (to the right of the number 9, and to the left of the “book”) and access the correct shape of the matrix you wish to enter. The first possible matrix template is for a 2×2 matrix. That is what I selected to enter my example matrix that you also see on the screen. If you wish to enter a 3×3 or larger square matrix, you will select the last matrix template shape (6th icon from the left, or the one just to the left of the sigma notation).
Now, see the image above to see the 2×2 matrix and its inverse that I typed into my TI-nspire. You will finish entering the four numbers inside the brackets, and press the ^ button, followed by -1. This does NOT mean the -1 power, it does NOT mean the reciprocal, in the context of a matrix, this symbol means INVERSE.
If you need to be able to find the inverse by hand….ask again for help!