Question

Let \(A\) be a \(3\times3\) matrix such that \[ \det(A)=-1. \] If \[ B^{-1}=Adj\!\left(A\,Adj(A^2)\right), \] then find \[ \det((\det A)B). \]

• A. \(|A|\)
• B. \(B\)
• C. \(|A+B|\)
• D. \(|A-B|\)

Hint:

For \(3\times3\) matrices, \[ Adj(A)=|A|A^{-1} \] is often the fastest route to simplify complicated determinant expressions.

Answer 1

The Correct Option is A