\( 1 \leftarrow \) Let \( A=\left[\begin{array}{ll}7 & 9 \\ 4 & 1\end{array}\right] \). Write 2A. Is \( \operatorname{det}(2 A) \) equal to \( 2 \operatorname{det}(A) \) ? \( 2 A=\left[\begin{array}{lr}14 & 18 \\ 8 & 2\end{array}\right] \) (Type an integer or decimal for each matrix element.) Select the correct choice below and fill in the answer box(es) to complete your choice. A. No, det(2A) is not equal to 2det(A). The value of det(2A) is \( \square \), whereas the value of 2det(A) is \( \square \). B. Yes, det(2A) is equal to 2det(A). The value of both expressions is \( \square \).

To determine whether \( \operatorname{det}(2A) \) is equal to \( 2 \operatorname{det}(A) \), we start by calculating \( \operatorname{det}(A) \). The determinant of matrix \( A \) is given by: \[ \operatorname{det}(A) = (7)(1) - (9)(4) = 7 - 36 = -29 \] Next, we compute \( \operatorname{det}(2A) \). The determinant of \( 2A \) can actually be calculated using the property of determinants, which states that \( \operatorname{det}(cA) = c^n \operatorname{det}(A) \), where \( n \) is the dimension of the square matrix. In this case, \( A \) is a \( 2 \times 2 \) matrix (so \( n = 2 \)), and we have: \[ \operatorname{det}(2A) = 2^2 \operatorname{det}(A) = 4(-29) = -116 \] Now let's compute \( 2 \operatorname{det}(A) \): \[ 2 \operatorname{det}(A) = 2(-29) = -58 \] Now, let’s fill in the answer based on our calculations: A. No, det(2A) is not equal to 2det(A). The value of det(2A) is \(-116\), whereas the value of 2det(A) is \(-58\).