fcad9c…: “Below the bitter ring”

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True/False: A square matrix $A$ is invertible if and only if $\det a \neq 1$ .

True False

What is $\det A$ if $\det A^T = 9$ .

$\answer {9}$

What is $\det AB$ if $\det A = 3$ and $\det B = 8$ .

$\answer {24}$

Let $A = \begin {bmatrix} a & b\\ c&d\end {bmatrix}$ and $\det A = 5$ . Find the determinant of
$B = \begin {bmatrix} 2a & 2b\\ c&d\end {bmatrix}$ .

$\answer {10}$

Let $A = \begin {bmatrix} a & b\\ c&d\end {bmatrix}$ and $\det A = 8$ . Find the determinant of
$B = \begin {bmatrix} c & d\\ a&b\end {bmatrix}$ .

$\answer {-8}$

Let $A = \begin {bmatrix} a & b\\ c&d\end {bmatrix}$ and $\det A = 3$ . Find the determinant of
$B = \begin {bmatrix} a & b\\ 4a+c&4b+d\end {bmatrix}$ .

$\answer {3}$