Question

Question:TRUE OR FALSE?If matrices A and Bare commute, then A must commute${\mathbf{B}}^{\mathbf{T}}$ withas well.

Short answer

The given statement is false.

Step-by-step solution

Definition of a commute.

Suppose A and Bare two matrices.

Then the matrices A and Bre said to be commute if AB = BA

Check whether the given statement is a true or false.

The given statement is if matrices A and B are commute, the A must commute with$B^T$ as well.

It is know that the matrix multiplication is not commutative.

So,$A{B}^T=B^{T}A$ is not true always.

Then the given statement is false.