If A is a non singular matrix of order 3,then|adj.A|=​

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If A is a non singular matrix of order 3,then|adj.A|=​

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Emery 1 week 2021-09-14T06:20:45+00:00 1 Answer 0 views 0

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    2021-09-14T06:22:13+00:00

    \textbf{Given:}

    \text{A is a non-singular matrix of order 3}

    \textbf{To find:}

    |adjA|

    \textbf{Solution:}

    \text{We know that,}

    \text{If A is a square matrix order n, then}

    \bf\,A(adjA)=(adjA)A=|A|\,I_n

    \implies\,(adjA)A=|A|\;I_n

    \text{Taking determinant}

    |(adjA)A|=||A|\;I_n|

    |adjA|\;|A|=|A|^n|I_n|

    |adjA|\;|A|=|A|^n(1)

    |adjA|\;|A|=|A|^n

    |adjA|=\dfrac{|A|^n}{|A|}

    \implies|adjA|=|A|^{n-1}

    \textbf{Answer:}

    \boxed{\bf|adjA|=|A|^{n-1}}

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