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Linear Algebra

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Moderate

Conjugacy Preserves Determinant

LINALG-XXJHNL

If $P$ is an invertible $2\times 2$ matrix and $A$ is a $2\times 2$ matrix then if:

$$PAP^{-1}=\begin{pmatrix} 2 & 7 \\\ 0 & 3\end{pmatrix}$$

...what is $\det(A)$?

A

$5$

B

$6$

C

$\cfrac{1}{6}$

D

It cannot be determined from the information given.