Assume that an economy is based on three industrial sectors: agriculture (A), building (B), and energy (E). The technology matrix M and final demand matrices (in billions of dollars) are

Given

Show that (I-M)-1(I-M) = 1

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A B E A 0.3 0.2 0.2 B | 0.1 0.1 0.11=M E L02 0.1 0.1 20 D10 D15 1.6 0.4 0.4 (I -M)10.22 1.18 0.18 0.38 0.22 1.22