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Consider a 3 × 3 matrix ? whose (i, j)-th element, ai, j = (i - j)3 Then the matrix A will be

Consider a 3 × 3 matrix ? whose (i, j)-th element, ai, j = (i - j)3 Then the matrix A will be Correct Answer skew-symmetric

Concept:

Square matrix A is said to be skew-symmetric if aij = -aji for all i and j.

In other words, we can say that matrix A is said to be skew-symmetric if the transpose of matrix A is equal to the negative of matrix A i.e, AT = -A.

Also, in a skew-symmetric matrix, the main diagonal elements are zero.

Explanation:

Given A = 3 × 3, aij = (i - j)3

To know about main diagonal elements, put i = j

∴ for i = j ⇒ aij = (i - i)3 = 0 ∀ i

For remaining elements, i ≠ j

∴ For i ≠ j ⇒ aij = (i - j)3 = (-(j - i))3

= -(j - i)3 = -aji

∴ Both the above conditions are satisfied.

Therefore matrix A is skew-symmetric matrix.

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