To find the determinant of the matrix [tex]\( B = \begin{pmatrix} 2 & 6 \\ -1 & 5 \end{pmatrix} \)[/tex], we use the formula for the determinant of a [tex]\( 2 \times 2 \)[/tex] matrix.
Given a matrix [tex]\( B = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \)[/tex], the determinant is calculated as:
[tex]\[
\text{det}(B) = ad - bc
\][/tex]
For the given matrix [tex]\( B \)[/tex]:
[tex]\[
a = 2, \quad b = 6, \quad c = -1, \quad d = 5
\][/tex]
Substituting these values into the determinant formula:
[tex]\[
\text{det}(B) = (2 \cdot 5) - (6 \cdot -1)
\][/tex]
[tex]\[
\text{det}(B) = 10 - (-6)
\][/tex]
[tex]\[
\text{det}(B) = 10 + 6
\][/tex]
[tex]\[
\text{det}(B) = 16
\][/tex]
Thus, the determinant of the matrix [tex]\( B \)[/tex] is 16. Therefore, the correct answer is:
[tex]\[
\boxed{16}
\][/tex]
