Question

For a matrix A, if a matrix B is obtained by changing its rows into columns and column into rows, then relation between A and B is?

(a) A^2 = B

(b) A^T = B

(c) Depends on the matrix

(d) None of the mentioned

I had been asked this question during an online interview.

Question is taken from Transpose of Matrices in section Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

The correct answer is (b) A^T = B

For explanation I would say: A = [aij] and B = [aji], B = A^T.