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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 & B are invertible matrices
|A| or |B|0
and |A|=2
(AB)1=16;|B|=?
since (AB)1=16
B1A1=16
B1A1=16
[(AB)1=B1A1(A1=1A)
(B1A1=B1A1)]
B112=16B1=13
|B|=1|B1|=3
|B|=3

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