# What are matrix multiplication not commutative?

## What are matrix multiplication not commutative?

In particular, matrix multiplication is not “commutative”; you cannot switch the order of the factors and expect to end up with the same result. (You should expect to see a “concept” question relating to this fact on your next test.) Given the following matrices, find the product BA.

Which algorithm is used for matrix multiplication?

Strassen algorithm
In linear algebra, the Strassen algorithm, named after Volker Strassen, is an algorithm for matrix multiplication.

### Is matrix multiplication always commutative?

Matrix multiplication is not commutative.

Why is matrix multiplication associative but not commutative?

Matrix multiplication is associative. Al- though it’s not commutative, it is associative. That’s because it corresponds to composition of functions, and that’s associative.

## Why is matrix not commutative?

The identity matrix commutes with all matrices. If the product of two symmetric matrices is symmetric, then they must commute. Circulant matrices commute. They form a commutative ring since the sum of two circulant matrices is circulant.

What is the fastest method for multiplication?

Schönhage–Strassen algorithm
The Schönhage–Strassen algorithm, developed by two German mathematicians, was actually the fastest method of multiplication from 1971 through 2007.

### What is the commutative property of multiplication?

The commutative property is a math rule that says that the order in which we multiply numbers does not change the product.

What order do you multiply 3 matrices?

You can “multiply” two 3 ⇥ 3 matrices to obtain another 3 ⇥ 3 matrix. Order the columns of a matrix from left to right, so that the 1st column is on the left, the 2nd column is directly to the right of the 1st, and the 3rd column is to the right of the 2nd.

## What makes a matrix commutative?

2.5.1 DIAGONAL MATRICES Multiplication of diagonal matrices is commutative: if A and B are diagonal, then C = AB = BA. iii. If A is diagonal, and B is a general matrix, and C = AB, then the ith row of C is aii times the ith row of B; if C = BA, then the ith column of C is aii times the ith column of B.