Matrices & Determinants
Determinant of Triple Adjoint of Scaled Matrix
nta_pyq_2023_apr
Grade 12
Question:
Let $A=\begin{pmatrix}2&1&0\\1&2&-1\\0&-1&2\end{pmatrix}$. If $|\text{adj}(\text{adj}(\text{adj}\,2A))|=(16)^n$, then $n$ is equal to
Step-by-Step Solution
Key Concept: $|\text{adj}(\text{adj}(\text{adj}\,A))|=|A|^{(n-1)^3}$ for $n\times n$ matrix. Here $n=3$. $|2A|=2^3|A|=8\times4=32$.
$|2A|=32$. $32^8=16^{10}$. $n=10$.
Correct Answer: 2