Question

If $A = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 1 & 1 \\ 1 & 3 & 1 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 3 & 4 \\ 3 & 2 & 2 \\ 2 & 4 & 2 \end{pmatrix}$, then $\sqrt{|\text{Adj}(AB)|} =$

• A. 176
• B. 208
• C. 198
• D. 234

Hint:

Remember the key properties of determinants and adjoints: $|\text{Adj}(M)| = |M|^{n-1}$ and $|AB| = |A||B|$. These properties save a significant amount of time compared to calculating the matrix product AB and then its adjoint.

Answer 1

The Correct Option is C