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| 1. |
For two non-singular matrices A&B, show that adj (AB)=adj(AB)=(adjB)(adjA) |
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Answer» Solution :We have (AB)(adj AB)=`|AB|I_(n)` `|A|=|B| I_(n)` `A^(-1)(AB)("adj"AB))=|A||B|A^(-1)` `Rightarrow B"adj"(AB)=|B|adjA(THEREFORE A^(-1)(1)/(|A|)adjA)` `Rightarrow B^(-1)B"adj"(AB)=|B|B^(-1)adjA` `Rightarrow B^(-1)B "adj"(AB)|B|B^(-1)"adj"A` `Rightarrow "adj"(AB)=("adj"B)("adjA")` |
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