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If AandB  are 3×3  matrices and |A|0,  then which of the following are true?

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a
|AB|=0   ⇒    |B|=0
b
|AB|=0   ⇒    B=0
c
|A−1|=  |A|−1
d
|A+A|=2|A|

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detailed solution

Correct option is A

For |AB|=0   ⇒   |A|  .  |B|=0   ⇒   |A|=0,   |B|=0       AA−1=I       ⇒    |A|  .   |A|−1=|I|=1   ⇒       |A−1|=1|A|=|A|−1

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