Question

Let $A=\begin{bmatrix}2& 1& -2\\ 1& 1& -1\\ 1& 0& 2\end{bmatrix}$ and if $B=|A|adj(A)$ Then $|B|$ is equal to

• A. 3
• B. 9
• C. 81
• D. 243

Hint:

The key formula here is $|k \cdot adj(A)| = k^n |A|^{n-1}$. For a $3 \times 3$ matrix, this becomes $k^3 |A|^2$. If $k = |A|$, the result is $|A|^3 |A|^2 = |A|^5$.

Answer 1

The Correct Option is D