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Question

If A and B are invertible matrices of order 3. |A|=2 and (AB)1=16. Find |B|

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Solution

|A|=2;(AB)1=16B1A1=16....(1)

|A|A1=1A1=1|A|=12.....(2)

from (1) and (2)

B1×12=16B1=13....(3)

|B|B1=1...(4)

from (3) and (4)

|B|(13)=1|B|=3

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