Chapter 11: Q. 4 (page 755)

True or False
Matrix multiplication is commutative.

Short Answer

Expert verified

False.

Step by step solution

Step 1. Given Information

Two matrices A & B.

Step 2. Calculation

$C o n s i d e r t w o m a t r i x A & B l e t A = [\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] B = [\begin{matrix} - 1 & 2 \\ 1 & - 3 \end{matrix}] A B = [\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} - 1 & 2 \\ 1 & - 3 \end{matrix}] = [\begin{matrix} - 1 + 2 & 2 - 3 \\ - 3 + 4 & 6 - 12 \end{matrix}] = [\begin{matrix} 1 & - 1 \\ - 1 & - 6 \end{matrix}] B A = [\begin{matrix} - 1 & 2 \\ 1 & - 3 \end{matrix}] [\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] = [\begin{matrix} - 1 + 6 & - 2 + 8 \\ 1 - 9 & 2 - 12 \end{matrix}] = [\begin{matrix} 5 & 6 \\ - 8 & - 10 \end{matrix}] A B \neq B A$

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True or False
Matrix multiplication is commutative.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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True or FalseMatrix multiplication is commutative.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Logic and Functions

Decision Maths

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

True or False
Matrix multiplication is commutative.