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  4. If A =[1 -1 1 0 2 -3 2 1 0], B =(adj A ) and C =5 A, then find (| adj B |/| C |)

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Q. If $A =\begin{bmatrix}1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0\end{bmatrix}, B =(adj A )$ and $C =5 A$, then find $\frac{| adj B |}{| C |}$

Matrices

Solution:

$| A |=5$
Now $|adj B|=|adj .(adj A)|$
$=| A |^ 4=5^{4}$
$|C|=|5 A |=5^{3}| A |=5^{4}$
$\therefore \frac{|adj . B |}{|C|}=1$