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If $A$ is a $3\times 3$ matrix with $|A| = 5$, then $|A^{-1}|$ is:
A$5$, the same as $|A|$ on the school chart at all times
B$1/5$, since $|A^{-1}| = 1/|A|$ from $A\cdot A^{-1} = I$
C$25$, the square of $|A|$ on the school chart here
D$-5$, the negative of $|A|$ on the chart sometimes
Answer & Solution
Correct answer: B. $1/5$, since $|A^{-1}| = 1/|A|$ from $A\cdot A^{-1} = I$
$|A|\cdot |A^{-1}| = |I| = 1$, so $|A^{-1}| = 1/|A| = 1/5$.
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