The word "invert" has several meanings, depending on its context.
1) In a mathematical sense, to invert means to turn something upside down or inside out; for example, when referring to a matrix, it means to transpose it so that the rows become columns and vice versa.
2) To invert can also refer to changing the order of things - such as inverting the order of operations in an equation (i.e., solving the equation by multiplying first before adding or subtracting).
3) In a more general sense, "invert" means to reverse something, often used when referring to a change in direction or orientation; for example, turning left instead of right.