Determinants

If \( A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} \), what is \( \det(A) \)?

For a 3x3 matrix \( B \), if two rows are identical, what is \( \det(B) \)?

If \( \det(A) = 7 \), what is \( \det(3A) \) for a 3x3 matrix \( A \)?

If \( A \) is a 2x2 matrix such that \( A^2 = I \) (identity matrix), what are the possible values of \( \det(A) \)?

Evaluate the determinant: \( \begin{vmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{vmatrix} \).

If \( A \) is a 3x3 matrix and \( \det(A) = 4 \), what is \( \det(A^{-1}) \)?

Given \( A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \), find \( \det(A) \).

If \( \det \begin{bmatrix} a & b \\ c & d \end{bmatrix} = 0 \) and \( a+d=5 \), which of the following could be the value of \( ad - bc \)?

If \( A = \begin{bmatrix} 1 & 0 & 2 \\ 3 & 1 & 0 \\ 4 & 0 & 1 \end{bmatrix} \), find \( \det(A) \).

If \( A \) is a 3x3 matrix with \( \det(A) = 5 \), find \( \det(2A^T) \).