| 1. If det \[A=0,\]then det \[(adj\,A)=0\] |
| 2. If A is non- singular, then \[\det \,({{A}^{-1}})={{(\det \,A)}^{-1}}\] |
A) 1 only
B) 2 only
C) Both 1 and 2
D) Neither 1 nor 2
Correct Answer: C
Solution :
[c] We know that, adj A and A has same value of determinant, if det A = 0, then det (adj A) = 0 So, statement (1) is correct. Also if A is a matrix the determinant of \[{{A}^{-1}}\] equals inverse of determinant A, so, det\[({{A}^{-1}})\] \[={{(detA)}^{-1}}\], if A is non-singular; statement 2 is correct. Thus both (1) and (2) are correct.
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