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Q15E

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Found in: Page 263

### Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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

The given statement is false.

See the step by step solution

## Step 1: Definition of a commute.

Suppose A and B are two matrices.

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

## Step 2: 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.