Question

If two rows of a determinant are identical, then what is the value of the determinant ?

• A. 0
• B. 1
• C. -1
• D. Can be any real value.

Answer 1

Answer: (A)

0

Let determinant of this matrix is $x$, if we interchange the two identical rows of the matrix then by property the determinant of the new matrix is $-x$, but overall the matrix will be same as we have interchanged only the two identical rows.

So, $x=-x$, we have $x=0$ .

Hence, the determinant is zero.