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An even number is the determinant of

(A) [1−1−15]\left[\begin{array}{rr}1 & -1 \\ -1 & 5\end{array}\right]

(B) [13−1−115]\left[\begin{array}{cc}13 & -1 \\ -1 & 15\end{array}\right]

(C) [16−1−1115]\left[\begin{array}{rr}16 & -1 \\ -11 & 15\end{array}\right]

(D) [6−121115]\left[\begin{array}{rr}6 & -12 \\ 11 & 15\end{array}\right]

Choose the correct answer from the options given below :

Solution

✅ Correct Option: 1

Determinant: det⁡[abcd]=ad−bc\det\begin{bmatrix}a&b\\c&d\end{bmatrix}=ad-bc.

(A) det⁡[1−1−15]=4\det\begin{bmatrix}1&-1\\-1&5\end{bmatrix}=4 even.

(B) det⁡[13−1−115]=194\det\begin{bmatrix}13&-1\\-1&15\end{bmatrix}=194 even.

(C) det⁡[16−1−1115]=229\det\begin{bmatrix}16&-1\\-11&15\end{bmatrix}=229 odd.

(D) det⁡[6−121115]=222\det\begin{bmatrix}6&-12\\11&15\end{bmatrix}=222 even.

Answer: (A), (B), & (D)

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