Determinant Practice Questions Ques3

Question: In a $3 \times 3$ matrix $A$, if the minor of $a_{11}$ is $5$, what is the cofactor of $a_{11}$?

Options:

(A) $5$

(B) $-5$

(C) $10$

(D) $-10$

Show Answer

Answer: A

Explanation:

(A) Correct. The cofactor of $a_{11}$ is $(-1)^{1+1} \times 5 = 5$.

(B) Incorrect. The sign is wrong.

(C) Incorrect. The value is wrong.

(D) Incorrect. Both the sign and value are wrong.