Let A be a non singular square matrix of order 3 - 3- Then adj A is equal to

We know that adj A = nbsp; A ^n 1 Where n is the order of matrix A Here, n = 3 adj A = nbsp; A ^3 1 ⇒ nbsp; adj A = A ^2 Hence, B is the correct answer ...

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Standard IX

Mathematics

Null Matrix

Let A be a no...

Question

Let $A$ be a non singular square matrix of order $3 \times 3$ . Then $| \begin{matrix} a d j A \end{matrix} |$ is equal to

3 | \begin{matrix} A \end{matrix} |

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| \begin{matrix} A \end{matrix} |

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{| \begin{matrix} A \end{matrix} |}^{2}

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{| \begin{matrix} A \end{matrix} |}^{3}

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Solution

The correct option is C ${| \begin{matrix} A \end{matrix} |}^{2}$
We know that $| \begin{matrix} a d j A \end{matrix} | = {| \begin{matrix} A \end{matrix} |}^{n - 1}$
Where $n$ is the order of matrix $A$
Here, $n = 3$
$| \begin{matrix} a d j A \end{matrix} | = {| \begin{matrix} A \end{matrix} |}^{3 - 1}$
$\Rightarrow | \begin{matrix} a d j A \end{matrix} | = {| \begin{matrix} A \end{matrix} |}^{2}$
Hence, $B$ is the correct answer.

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Null Matrix

Standard IX Mathematics

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Let A be a non singular square matrix of order 3×3. Then |adj A| is equal to

The correct option is C |A|2We know that |adj A|=|A|n−1 Where n is the order of matrix A Here, n=3 |adj A|=|A|3−1 ⇒|adj A|=|A|2 Hence, B is the correct answer.

Let $A$ be a non singular square matrix of order $3 \times 3$ . Then $| \begin{matrix} a d j A \end{matrix} |$ is equal to