# eigen value

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1
331776 ??
0

yes @ joshi_nitish

Matrices Have Property

If a Matrix is square of order n then $\left | Adj A \right |=\left ( det A \right )^{n-1}=\left | A \right |^{n-1}$

Similarly $\left | Adj\left ( Adj A \right ) \right |=\left | A \right |^{\left ( n-1 \right )^{2}}$

Another Property is Product of Eigen Values = Determinant of matrix

Product of Eigen values = 24

$\left | Adj\left ( Adj A \right ) \right |=\left | 24 \right |^\left ( 3-1 \right ){^{2}}$=$\left | 24 \right |^{4}$= 331776

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we know that $\left | adj\left ( adj\left ( A \right ) \right ) \right |= \left | A \right |^{\left ( n-1 \right )}^{2 }$

and we know that $|A|=\prod \lambda _{i}$  which $\lambda _{i}$  are the eigenvalue of A.

determinant of A is 24 and $(24)^{2^{2}}$ =$(24)^4=331776$

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