Question

Which of the following is not the property of transpose of a matrix?

(a) (A’)’=A

(b) (A+B)’=A’+B’

(c) (AB)’=(BA)’

(d) (kA)’=KA’

This question was posed to me by my college professor while I was bunking the class.

I need to ask this question from Transpose of a Matrix topic in chapter Matrices of Mathematics – Class 12

Answer 1

Right option is (c) (AB)’=(BA)’

To elaborate: (AB)’=(BA)’is incorrect. We know that matrix multiplication is not commutative i.e. AB≠BA. Hence, its transpose will also not be commutative.

(AB)’=B’A’