The multiplicative inverse, or reciprocal, of a number "x", is "1/x". For example, the multiplicative inverse of 5 is 1/5. For a fraction, just exchange numerator and denominator. For example, the multiplicative inverse of 2/5 is 5/2.
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Matrix inverses and determinants, square and nonsingular, the equations AX = I and XA = I have the same solution, X. This solution is called the inverse of A.
Tell me the equations first.
You need as many equations as you have variables.
You can solve the system of equations with three variables using the substitute method, or using matrix operations.
If you don't learn to solve equations then guess and check is the only way to arrive at new information.