Finding a Production Matrix
To obtain the production matrix, X, for an open input-output model, follow these steps:
a. Form the n 
n input-output matrix, A, by placing in each column the amount of the various commodities required to produce 1 unit of a particular commodity.
b. Calculate I – A, where is the n n identity matrix.
c. Find the inverse, (I – A)-1.
d. Multiply the inverse on the right by the demand matrix, A, to obtain X = (I- A)-1 D.
To obtain a production matrix, X, for a closed input-output model, solve the system (I – A) X = 0.