Matrices & Determinants
Matrix Operations
MMTS_Full_Test_11
Grade 12
Question:
If $A$ is matrix of order 3 such that $|A|=5$ and $B=\text{adj}\,A$, then the value of $\left\||A^{-1}|(AB)^T\right\|$ is equal to
Step-by-Step Solution
Key Concept: $B=\text{adj}A$, so $AB=A\cdot\text{adj}A=|A|I$
$AB=|A|I=5I$. $(AB)^T=5I$. $|A^{-1}|=1/5$. $|A^{-1}||AB|^T=\frac{1}{5}\cdot 5^3 = 25$.
Correct Answer: 3