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Question

If A and B are invertible matrices of order 2, |A| =2 and |(AB)1|=16, find |B|.

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Solution

As |P1|=1|P||(AB)1|=1|AB|=1|A||B|=12×|B|

Also since |(AB)1|=16 so, 12×|B|=16|B|=3.

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