Unformatted text preview: D = C1 B1 A1 . Then D ( ABC ) = C1 B1 ( A1 A ) BC = C1 B1 ( I n ) BC = C1 ( B1 B ) C = C1 ( I n ) C = C1 C = I n and ( ABC ) D = AB ( CC1 ) B1 A1 = AB ( I n ) B1 A1 = A ( BB1 ) A1 = A ( I n ) A1 = AA1 = I n . i.e., D ( ABC ) = I n = ( ABC ) D . Thus, ABC is invertible and D = C1 B1 A1 is the inverse. 1...
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 Fall '06
 Sze
 Matrices, Existence, Invertible matrix, Multiplicative inverse

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