Question

If the matrices $A = \begin{bmatrix}1&1&2\\ 1&3&4\\ 1&-1&3\end{bmatrix}$, B = adj A and C = 3A , then $\frac{\left|adj\,B\right|}{\left|C\right|}$ is equal to :

• A. 16
• B. 2
• C. 8
• D. 72

Answer 1

Answer: (C)

$A = \begin{bmatrix}1&1&2\\ 1&3&4\\ 1&-1&3\end{bmatrix}$
$\Rightarrow \left|A\right|=6$
$\frac{\left|adj\,B\right|}{\left|c\right|}=\frac{\left|adj\left(adj\,A\right)\right|}{\left|9\,A\right|}=\frac{\left|A\right|^{4}}{3^{3}\left|A\right|}=\frac{\left|A\right|^{3}}{3^{3}}$
$=\frac{\left(6\right)^{3}}{\left(3\right)^{3}}=8$