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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?

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 the condition for AB BA in matrix?

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.

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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 difference between AB and BA in matrix theory?

For example, if A = cI where I is the identity matrix, then AB = BA for all matrices B. In fact, the converse is true: If A is an n × n matrix such that AB = BA for all n × n matrices B, then A = cI for some constant c. Therefore, if A is not in the form of cI, there must be some matrix B such that AB ≠ BA. Share.

What is the product of A and B in matrices?

If A and B be any two matrices, then their product AB will be defined only when the number of columns in A is equal to the number of rows in B. AB e BA. AB  = BA.

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What is the Order of matrix (5A – 2B)?

If A and B are two matrices of the orders 3 × m and 3 × n, respectively, and m = n, then the order of matrix (5A – 2B) is If A, B are square matrices of same order and B is a skew – symmetric matrix. Show that if A and B are square matrices such that AB = BA, then (A+B)2 = A2 + 2AB + B2 .

Can A and B be both diagonal matrices?

A and B are both diagonal matrices. There exists an invertible matrix P such that P − 1 A P and P − 1 B P are both diagonal. There is actually a sufficient and necessary condition for M n ( C):