Question

If $A=\left|\begin{array}{ccc}1& -1& 1\\ 0& 2& -3\\ 2& 1& 0\end{array}\right|$ and $B=\left(adjA\right)$, and $C=5A$, then $\frac{|adjB|}{|C|}$ is?

• A. $5$
• B. $25$
• C. $-1$
• D. $1$

Answer 1

The correct option is D $1$

$|adj\left(A\right)|=|A{|}^{n-1}\dots eqn\left(1\right)$ (property of adjoint of matrix)

$|A|=1\left(3\right)+1\left(6\right)+1(-4)=5\dots eqn\left(2\right)$

from the eqn (1) and (2)

$|B|=5^{3-1}=5^2$

$\frac{|adj\left(B\right)|}{|C|}=\frac{5^2}{5\times 5}=1$