Matrices & Determinants
Determinant Properties
MMTS_Full_Test_13
Grade 12
Question:
If $A$ is a square matrix of order 3 such that $\det(A)=3$ and $\det(adj(-4\cdot adj(-3\cdot adj(3\cdot adj((2A)^{-1})))))=2^m3^n$. Then $m+2n$ is equal to
Step-by-Step Solution
Key Concept: Use $\det(adj(A))=|A|^{n-1}$ for $n\times n$ matrix; $\det(kA)=k^n\det A$
Working outward step by step: $m+2n=4$.
Correct Answer: 4