To calculate the inverse of a square matrix on a TI-83, use the notation A^(-1), ensuring that the -1 is enclosed in parentheses. This method is similar to finding the multiplicative inverse of a number. Users should double-check that the matrix is square and invertible before attempting the calculation. It's also advisable to familiarize oneself with the matrix functions on the calculator for efficient use. Mastering this technique can help in solving quiz problems involving matrix inverses.