Math Help - Economic matrices Which sector produces the greatest dollar value to meet the demand?

1. Economic matrices Which sector produces the greatest dollar value to meet the demand?

Consider an economy with three product-producing sectors and one non-producing sector. Suppose the
economy is described by the Leontief equation with consumption matrix

If the open sector demands the same dollar value from each product-producing sector, which sector
must produce the greatest dollar value to meet the demand?

A hint that was given to me,although I don't think it isvery relevant: "You may use the fact that (A/a)−1 = aA−1 for any invertible matrix A and any nonzero a ∈ R."