Question

Let A = [aij] given by abij = (i-j)^3 is a _________

(a) Symmetric matrix

(b) Anti-Symmetric matrix

(c) Identity matrix

(d) None of the mentioned

This question was addressed to me during an interview for a job.

This is a very interesting question from Transpose of Matrices in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

Right answer is (b) Anti-Symmetric matrix

The explanation is: aji =(j-i^3) = -aij, A is Anti-symmetric matrix.