If $A$ is a $3 imes 3$ matrix with $|A| = 5$, then $|A^{-1}|$ is:

Question

If $A$ is a $3	imes 3$ matrix with $|A| = 5$, then $|A^{-1}|$ is:

Accepted Answer

B. $1/5$, since $|A^{-1}| = 1/|A|$ from $A\cdot A^{-1} = I$

$|A|\cdot |A^{-1}| = |I| = 1$, so $|A^{-1}| = 1/|A| = 1/5$.

Answer

$5$, the same as $|A|$ on the school chart at all times

Answer

$25$, the square of $|A|$ on the school chart here

Answer

$-5$, the negative of $|A|$ on the chart sometimes

If $A$ is a $3\times 3$ matrix with $|A| = 5$, then $|A^{-1}|$ is: