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If `A` is non-diagonal involuntary matrix, then a. `A-I=O` b. `A+I=O` c. `A-I` is nonzero singular d. none of these

A

`A-I=O`

B

`A+I=O`

C

`A-I` is nonzero singular

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`A^(2)=I`
or `A^(2)-I=O`
or `(A+I) (A-I)=0`
therefore, either `|A+I|=0` or `|A-I|=0`. If `|A-I| ne 0`, then `(A+I) (A-I)=Oimplies A+I=O` which is not so.
`:. |A-I|=0` and `A-I ne O`
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