Unformatted text preview: D = C-1 B-1 A-1 . Then D ( ABC ) = C-1 B-1 ( A-1 A ) BC = C-1 B-1 ( I n ) BC = C-1 ( B-1 B ) C = C-1 ( I n ) C = C-1 C = I n and ( ABC ) D = AB ( CC-1 ) B-1 A-1 = AB ( I n ) B-1 A-1 = A ( BB-1 ) A-1 = A ( I n ) A-1 = AA-1 = I n . i.e., D ( ABC ) = I n = ( ABC ) D . Thus, ABC is invertible and D = C-1 B-1 A-1 is the inverse. 1...
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- Fall '06
- Matrices, Existence, Invertible matrix, Multiplicative inverse