Why is matrix AB not equal to BA?

Why is matrix AB not equal to BA?

Since matrix multiplication is not commutative, BA will usually not equal AB, so the sum BA + AB cannot be written as 2 AB. In general, then, ( A + B) ≠ A 2 + 2 AB + B 2.

Is AB matrix is equal to BA matrix?

The product of matrices A and B is defined if the number of columns in A matches the number of rows in B. Any of the above identities holds provided that matrix sums and products are well defined. If A and B are n×n matrices, then both AB and BA are well defined n×n matrices. However, in general, AB = BA.

Is matrix multiplication commutative ie for any matrix A and B AB BA?

Since A B ≠ B A AB\neq BA AB=BAA, B, does not equal, B, A, matrix multiplication is not commutative! Other than this major difference, however, the properties of matrix multiplication are mostly similar to the properties of real number multiplication.

What is the condition for diagonal matrix?

A matrix is diagonal if and only if it is triangular and normal. A matrix is diagonal if and only if it is both upper- and lower-triangular. A diagonal matrix is symmetric.

Why is AB not a BA?

In all the non-abelian groups(i.e., groups that do not commute), a*b is not equal to b*a. Basically a non empty set ‘G’ with a binary operation * is a group, if it satisfies the following properties: Closure: If ‘a’ and ‘b’ belong to G, the a*b also belongs to G. Associative: a*(b*c) = (a*b)*c.

Is AB BA True or false?

If AB and BA both exist, then AB = BA False.

Is AB BA in sets?

To denote the DIFFERENCE of A and be we write: A-B or B-A. A-B is the set of all elements that are in A but NOT in B, and B-A is the set of all elements that are in B but NOT in A. Notice that A-B is always a subset of A and B-A is always a subset of B.

What is the necessary condition for the product AB BA if the matrices A and B to be both defined and to be both equal?

From (4) and (5), we can conclude that A and B are square matrices and their orders are one and the same. Thus, for both addition and multiplication of two matrices to be possible, it is required that both the matrices should be of same order and they should be square matrices.

What is diagonal and off-diagonal matrix?

In a table of numbers that has the same number of rows as columns, the entries that are not in the Main Diagonal are referred to as the off-diagonal entries in the table. In this example, all the 0s are in the off-diagonal cells.

Which of the following is not a necessary condition for a matrix say A to be diagonalizable?

1. Which of the following is not a necessary condition for a matrix, say A, to be diagonalizable? Explanation: The theorem of diagonalization states that, ‘An n×n matrix A is diagonalizable, if and only if, A has n linearly independent eigenvectors.

How do you find AB not equal to BA?

hope you get your answer…. When you define something like a*b=a+2b then a*b is not equal to b*a where b*a=b+2a which is possible only when a =b.

Are the two matrices AB and Ba equal?

The two matrices AB and BA are not equal and that’s it. You would probably not go asking what is the logic behind Batman and Superman not being equal (and there is no reason to treat matrices differently that superheroes, really)$endgroup$

Is it true that $ab = ba?

It simply isn’t true that $AB = BA$, except in very special cases, such as if both $A$ and $B$ are diagonal.

Is AB = P(Ba) a symmet- Ric polynomial?

Any p with p(AB) = p(BA) is a similarity invariant, so gives the same values if we permute the diagonal entries. Therefore it is a symmet- ric polynomial in the eigenvalues. n,n), on diagonal matrices.