TS ICET 24 May 2018 Shift 1 Paper

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Question : 132 of 200

Marks: +1, -0

Let |5| denote the determinant o f any matrix S. If A is a 3x3 matrix, then |Adj(Adj

\A^2)

| =

$|\A|^2$
$|\A|^4$
$|\A|^8$
$|\A|^16$

Solution:

Let

A^2=C

and Adj

\A^2=

Adj C = B

|\Adj(\Adj A^{2})|=|\Adj B|=|B|^{2}

| B |=|\Adj C |=| C |^{2}=| A ^{2}|^{2}=| A |^{4}

∴ \Adj(\Adj A^{2})=|B|^{2}=|A^{4}|^{2}=|A|^{8}

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