Question

For a given matrix A of 3 x 3 order, find |Adj(A)|
Where, $A=\left[\begin{array}{ccc}1& 2& 1\\ 0& 5& 1\\ 1& 4& 3\end{array}\right]$

• A. 8
• B. 32
• C. 64
• D. 512

Answer 1

The correct option is C 64

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

Where n is order of A,

Now,
$|A|=1\left|\begin{array}{cc}5& 1\\ 4& 3\end{array}\right|+0+1\left|\begin{array}{cc}2& 1\\ 5& 1\end{array}\right|$

$\Rightarrow |A|=11-3$
$\Rightarrow |A|=8$

Using (1),

$|Adj\left(A\right)|=8^{3-1}=8^2=64$