If A=[ 1 2 3 4 5 6 ] and B=[ 1 4 2 5 3 6 ], then the determinant value of BA is

Question

If A=[ 1 2 3 4 5 6 ] and B=[ 1 4 2 5 3 6 ], then the determinant value of BA is (A) 8 (B) 0 (C) -8 (D) 24

Tardigrade Admin · Accepted Answer

BA=[ 1 4 2 5 3 6 ][ 1 2 3 4 5 6 ]=[ 17 22 27 22 29 36 27 36 45 ] |B A|=| 17 5 5 22 7 7 27 9 9 | (Using C3 arrow C3-C2 and C2 arrow C2-C1 ) Hence, |B A|=0

Q. If $A = [142536]$ and $B = ⎣ ⎡ 123456 ⎦ ⎤,$ then the determinant value of $B A$ is

$8$

$0$

$- 8$

$24$

$B A = ⎣ ⎡ 123456 ⎦ ⎤ [142536] = ⎣ ⎡ 172227222936273645 ⎦ ⎤$
$∣ B A ∣ = ∣ ∣ 172227579579 ∣ ∣$ (Using $C_{3} \to C_{3} - C_{2}$ and $C_{2} \to C_{2} - C_{1}$ )
Hence, $∣ B A ∣ = 0$

Q. If A=[14​25​36​] and B=⎣⎡​123​456​⎦⎤​, then the determinant value of BA is

8

0

−8

24

BA=⎣⎡​123​456​⎦⎤​[14​25​36​]=⎣⎡​172227​222936​273645​⎦⎤​ ∣BA∣=∣∣​172227​579​579​∣∣​ (Using C3​→C3​−C2​ and C2​→C2​−C1​ ) Hence, ∣BA∣=0

Q. If $A = [142536]$ and $B = ⎣ ⎡ 123456 ⎦ ⎤,$ then the determinant value of $B A$ is

$8$

$0$

$- 8$

$24$

$B A = ⎣ ⎡ 123456 ⎦ ⎤ [142536] = ⎣ ⎡ 172227222936273645 ⎦ ⎤$
$∣ B A ∣ = ∣ ∣ 172227579579 ∣ ∣$ (Using $C_{3} \to C_{3} - C_{2}$ and $C_{2} \to C_{2} - C_{1}$ )
Hence, $∣ B A ∣ = 0$