Question

If $A = \begin{pmatrix} 1 & 5 & 2 \\ 4 & 1 & 3 \\ 2 & 6 & 3 \end{pmatrix}$, then $|(\text{Adj A})^{-1}| =$

• A. -1
• B. 1
• C. 4
• D. -4

Hint:

This problem is solved efficiently by knowing determinant properties. Direct calculation of the adjoint, its inverse, and then its determinant would be extremely time-consuming. Always look for ways to use properties like $|M^{-1}|=1/|M|$ and $|\text{Adj A}|=|A|^{n-1}$.

Answer 1

The Correct Option is B