Is Matrix AB the same as BA?

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Is Matrix AB the same as BA?

In general, AB = BA, even if A and B are both square. If AB = BA, then we say that A and B commute. For a general matrix A, we cannot say that AB = AC yields B = C.

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.

How do you know if a matrix product is defined?

When is matrix multiplication defined? In order for matrix multiplication to be defined, the number of columns in the first matrix must be equal to the number of rows in the second matrix. To find A B AB AB , we take the dot product of a row in A and a column in B.

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Is AB BA give reason?

Answer:This is only applicable when a is equal to b. Step-by-step explanation:If a is not equal to b then the statement will not hold.

How to prove that A and B are square commuting matrices?

One direction is obvious. The other direction, we need to show that if ( A B) T = A T B T, then A and B are square commuting matrices. AB is defined, so n C o l ( A) = n R o w ( B).

How do you find the transpose of a matrix?

· The transpose of the transpose of a matrix is the matrix itself: (AT)T = A · Transpose of a scalar multiple: The transpose of a matrix times a scalar (k) is equal to the constant times the transpose of the matrix: (kA)T = kAT · Transpose of a sum: The transpose of the sum of two matrices is equivalent to the sum of their transposes:

Where can I find the meaning of the indices of matrices?

For matrices, appears in https://www.maa.org/sites/default/files/0746834207570.di020741.02p0009e.pdf, where you will find the meaning for the various indices and symbols.

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Do matrices have to be of compatible size to multiply?

The matrices have to be of compatible size to be multiplied, but after that, it’s true, and they don’t need to commute. With these sorts of questions it’s often best to just go to the dictionary of math, the definitions, and restate the question by wording it in a way that eschews the fancy but terse terminology.