Question:
Which of the following is not correct in a given determinant of $A$, where $A=\left[a_{i}\right]_{3 \times 3}$.
(a) Order of minor is less than order of the det (A)
(b) Minor of an element can never be equal to cofactor of the same element
(c) Value of determinant is obtained by multiplying elements of a row or column by corresponding cofactors
(d) Order of minors and cofactors of elements of $A$ is same
Solution:
(b) Minor of an element can never be equal to the cofactor of the same element.
$C_{i j}=(-1)^{i+j} M_{i j}$
So, for even values of $i+j, C_{i j}=M_{i j}$.
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