An even number is the determinant of
(A) $\left[\begin{array}{rr}1 & -1 \\ -1 & 5\end{array}\right]$
(B) $\left[\begin{array}{cc}13 & -1 \\ -1 & 15\end{array}\right]$
(C) $\left[\begin{array}{rr}16 & -1 \\ -11 & 15\end{array}\right]$
(D) $\left[\begin{array}{rr}6 & -12 \\ 11 & 15\end{array}\right]$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (D) only
$(A)\;\begin{vmatrix}1&-1\\-1&5\end{vmatrix}=1\cdot5-(-1)(-1)=5-1=4.$
$(B)\;\begin{vmatrix}13&-1\\-1&15\end{vmatrix}=13\cdot15-1=195-1=194.$
$(C)\;\begin{vmatrix}16&-1\\-11&15\end{vmatrix}=16\cdot15-(-1)(-11)=240-11=229.$
$(D)\;\begin{vmatrix}6&-12\\11&15\end{vmatrix}=6\cdot15-(-12)(11)=90+132=222.$
$\text{Even determinants are }4,194,222.$
$\text{Correct options: (A),(B),(D).}$