Determinants

What is the value of the determinant \( \begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix} \)?

If \( A = \begin{bmatrix} 3 & 0 \\ 0 & 5 \end{bmatrix} \), what is \( \det(A) \)?

Which of the following properties of determinants is TRUE?

Find the determinant of \( \begin{vmatrix} 2 & 3 & 1 \\ 4 & 1 & -3 \\ 1 & 2 & 5 \end{vmatrix} \).

If \( \det(A) = 5 \), what is \( \det(3A) \) for a 3x3 matrix \(A\)?

The determinant of \( \begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 6 \end{bmatrix} \) is:

If \( \det \begin{bmatrix} a & b \\ c & d \end{bmatrix} = 0 \), then the vectors \( \begin{bmatrix} a \\ c \end{bmatrix} \) and \( \begin{bmatrix} b \\ d \end{bmatrix} \) are:

Evaluate the determinant \( \begin{vmatrix} 1 & 0 & 2 \\ 3 & 1 & 0 \\ 4 & 2 & 1 \end{vmatrix} \).

If \( \det(A) = 7 \), find \( \det(A^{-1}) \).

Given \( A = \begin{bmatrix} 2 & 3 & 1 \\ 4 & 1 & -3 \\ 1 & 2 & 5 \end{bmatrix} \), find the value of \( \det(2A) \).