(a) Let A be an n × n matrix whose entries are all very small, |Aij| 1/n, and let I be the unit matrix. Show that
(I + A)ˆ’1 = I ˆ’ A + A2 ˆ’ A3 + A4 ˆ’ +. . .
By proving that (i) the series on the right-hand side converges absolutely for each of the n2 entries, and (ii) (I + A) times the right-hand side equals I.
(b) Use (a) to establish Eq. (8.21) from Eq. (8.20).

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arr (8.20) (8.21)