The value of the determinant of a 3x3 matrix where each element a_ij is defined as i+j is:

A. 0 — Construct the matrix and observe the linear dependence between rows or columns. If rows are in arithmetic progression, the determinant is zero.

JEE Main · MathematicsMedium

$The value of the determinant of a 3 \times 3 matrix where each element a_{ij} is defined as i + j is:$

A. $0$
B. $1$
C. $- 1$
D. $3$

Show correct answer & step-by-step solution

Correct answer: A — $0$

Solution

The matrix is 234345456 . Since R_{2} - R_{1} = R_{3} - R_{2}, the rows are linearly dependent, so the determinant is 0 .

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The value of the determinant of a 3×3 matrix where each element aij​ is defined as i+j is:

Solution

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$The value of the determinant of a 3 \times 3 matrix where each element a_{ij} is defined as i + j is:$