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If A and B are 3xx3 matrices and abs(A)n...

If A and B are `3xx3` matrices and `abs(A)ne 0,` which of the
following are true?

A

`abs(AB)=0rArr abs(B) = 0`

B

`abs(AB)ne 0rArr abs(B)ne = 0`

C

`abs(A^(-1) ) = abs(A)^-1`

D

`abs(A+A) = 2 abs(A)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`abs(AB) = 0 rArr abs(A) abs(B) = 0`
`therefore abs(B) = 0 " as "abs(A) ne 0`
Also, `abs(A^(-1)) = abs(A)^(-1)`
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