If any two rows (or columns) of a determinant are identical (all corresponding elements are same), then the value of determinant is

Question

If any two rows (or columns) of a determinant are identical (all corresponding elements are same), then the value of determinant is (A) 1 (B) -1 (C) 0 (D) 2

Tardigrade Admin · Accepted Answer

If we interchange the identical rows (or columns) of the determinant Δ, then numerical value of Δ does not change but due to interchange, the sign of Δ will change. ∴ Δ=-Δ ⇒ Δ=0

Q. If any two rows (or columns) of a determinant are identical (all corresponding elements are same), then the value of determinant is

1

-1

0

2

If we interchange the identical rows (or columns) of the determinant $Δ$ , then numerical value of $Δ$ does not change but due to interchange, the sign of $Δ$ will change.
$∴ Δ = - Δ \Rightarrow Δ = 0$

Q. If any two rows (or columns) of a determinant are identical (all corresponding elements are same), then the value of determinant is

1

-1

0

2

If we interchange the identical rows (or columns) of the determinant Δ, then numerical value of Δ does not change but due to interchange, the sign of Δ will change. ∴Δ=−Δ⇒Δ=0

If we interchange the identical rows (or columns) of the determinant $Δ$ , then numerical value of $Δ$ does not change but due to interchange, the sign of $Δ$ will change.
$∴ Δ = - Δ \Rightarrow Δ = 0$