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Multiplication of 2x2 matrices is commutative?

Updated: 4/28/2022

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∙ 11y ago

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No. Multiplication of matrices is, in general, non-commutative, due to the way multiplication is defined.

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Q: Multiplication of 2x2 matrices is commutative?

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Continue Learning about Other Math

Multiplication of 2 X 2 matrices is commutative?

Sometimes . . A+

What are multiplication properties?

The answer depends on the context. For example, multiplication of numbers is commutative (A*B = B*A) but multiplication of matrices is not.

What property is illustrated by this problem 7x8 equals 8x7?

The Abelian or commutative property of the multiplication of numbers. It is important that both "multiplication" and "numbers" feature in the answer. Because, it is applicable to multiplication but not, for example, for division. It is applicable for the multiplication on numbers but not matrices.

Are there Exceptions to the commutative property?

The commutative property works for adding and multiplying e.g. 2+4=4+2 and 3x4=4x3. But it doesn't work for subtraction and division so 5-3≠3-5 and 6÷2≠2÷6 so subtraction and division could be considered as exceptions.

Why AxB is not equal to BxA?

It is so too equal! Multiplication is commutative. Unless A and B are matrices. Matrix multiplication is NOT commutative. Whether or not AxB = BxA depends upon the definition of the binary operator x [multiply] in the domain over which it is defined.

Related questions

Are matrix addition and matrix multiplication commutative?

Matrix addition is commutative if the elements in the matrices are themselves commutative.Matrix multiplication is not commutative.

Multiplication of 2 X 2 matrices is commutative?

Sometimes . . A+

Which operatoins are not commutative?

Subtraction, division, cross multiplication of vectors, multiplication of matrices, etc.

What is the deffinition of commutative?

Assuming you mean definition, commutative is a property of an operation such that the order of the operands does not affect the result. Thus for addition, A + B = B + A. Multiplication of numbers is also commutative but multiplication of matrices is not. Subtraction and division are not commutative.

What are multiplication properties?

The answer depends on the context. For example, multiplication of numbers is commutative (A*B = B*A) but multiplication of matrices is not.

What property is illustrated by this problem 7x8 equals 8x7?

The Abelian or commutative property of the multiplication of numbers. It is important that both "multiplication" and "numbers" feature in the answer. Because, it is applicable to multiplication but not, for example, for division. It is applicable for the multiplication on numbers but not matrices.

Is Multiplication communicative?

The multiplication most people are familiar with which you probably learned in school, IS commutative - that's the multiplication of integers, as well as real numbers in general.There are some other operations which mathematicians call "multiplication" which are NOT communitative; for example, the multiplication of matrices, or the cross-product of vectors.

Is the set of all 2x2 invertible matrices a subspace of all 2x2 matrices?

I assume since you're asking if 2x2 invertible matrices are a "subspace" that you are considering the set of all 2x2 matrices as a vector space (which it certainly is). In order for the set of 2x2 invertible matrices to be a subspace of the set of all 2x2 matrices, it must be closed under addition and scalar multiplication. A 2x2 matrix is invertible if and only if its determinant is nonzero. When multiplied by a scalar (let's call it c), the determinant of a 2x2 matrix will be multiplied by c^2 since the determinant is linear in each row (two rows -> two factors of c). If the determinant was nonzero to begin with c^2 times the determinant will be nonzero, so an invertible matrix multiplied by a scalar will remain invertible. Therefore the set of all 2x2 invertible matrices is closed under scalar multiplication. However, this set is not closed under addition. Consider the matrices {[1 0], [0 1]} and {[-1 0], [0 -1]}. Both are invertible (in this case, they are both their own inverses). However, their sum is {[0 0], [0 0]}, which is not invertible because its determinant is 0. In conclusion, the set of invertible 2x2 matrices is not a subspace of the set of all 2x2 matrices because it is not closed under addition.

What happens to the product when you change the grouping of three factors in a multiplication problem?

Nothing. Multiplication is commutative and associative.Nothing. Multiplication is commutative and associative.Nothing. Multiplication is commutative and associative.Nothing. Multiplication is commutative and associative.

Are there Exceptions to the commutative property?

The commutative property works for adding and multiplying e.g. 2+4=4+2 and 3x4=4x3. But it doesn't work for subtraction and division so 5-3≠3-5 and 6÷2≠2÷6 so subtraction and division could be considered as exceptions.

Why AxB is not equal to BxA?

It is so too equal! Multiplication is commutative. Unless A and B are matrices. Matrix multiplication is NOT commutative. Whether or not AxB = BxA depends upon the definition of the binary operator x [multiply] in the domain over which it is defined.

Matrix multiplication is not commutative?

That is true, matrix multiplication is not commutative.

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