Question

(A B C)^T = _______

(a) (C B A)^T

(b) B^T C^T A^T

(c) C^T B^T A^T

(d) A^T B^T C^T

I had been asked this question during a job interview.

My doubt is from Matrix Algebra topic in chapter Matrix Algebra and Gaussian Elimination of Finite Element Method

Answer 1

The correct answer is (c) C^T B^T A^T

To explain I would say: A matrix which is formed by turning all the rows of given matrix into columns and vice versa is called a transpose of matrix. The transpose of a product is given as the product of the transposes in the reverse order.

(A B C)^T = C^T B^T A^T.