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

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Question: Answered & Verified by Expert

If

A = [\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{matrix}]

and

B = [\begin{matrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{matrix}],

then the determinant value of

B A

is

MathematicsDeterminantsJEE Main

Options:

A $8$
B $0$
C $- 8$
D $24$

Solution:

2172 Upvotes Verified Answer

The correct answer is:

0

B A = [\begin{matrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{matrix}] [\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{matrix}] = [\begin{matrix} 17 & 22 & 27 \\ 22 & 29 & 36 \\ 27 & 36 & 45 \end{matrix}]

|B A| = |\begin{matrix} 17 & 5 & 5 \\ 22 & 7 & 7 \\ 27 & 9 & 9 \end{matrix}|

(Using

C_{3} \to C_{3} - C_{2}

and

C_{2} \to C_{2} - C_{1}

)
Hence,

|B A| = 0

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