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Let A,B and C be nxxn matrices. Which on...

Let `A,B` and `C` be `nxxn` matrices. Which one of the following is a correct statement?

A

If `AB=AC` then `B=C`

B

If `A^(3)+2A^(2)+3A+5l=O` then A is invertible

C

If `A^(2)=O` then `A=O`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
A
`AB=AC` premultiply by `A^(-1)` we get
`A^(-1)AB=A^(-1)AC`
`B=C [ :' "AA"^(-1)=1]`
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