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TheScienceAlliance
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If A and B are matrices that AC = AC and BC=CB, where C is a matrix whose first row's entries are 0 1 and the second row's entries are -1 0, then AB=BA.
Is there a typo? Did you mean AC = CA?MathHelpBoardsUser said:If A and B are matrices that AC = AC and BC=CB, where C is a matrix whose first row's entries are 0 1 and the second row's entries are -1 0, then AB=BA.
Yes. I apologize.topsquark said:Is there a typo? Did you mean AC = CA?
-Dan
The "Matrix: True or False? AB=BA" question is a mathematical question that asks whether the product of two matrices, AB, is equal to the product of the same matrices in reverse order, BA. In other words, does the order of multiplication matter in matrix multiplication?
This question is important because it tests the commutative property of matrix multiplication. If AB=BA is true, then matrix multiplication is commutative, meaning that the order of multiplication does not affect the result. This has significant implications in various fields, including physics, engineering, and computer science.
The answer to this question is that it depends on the matrices being multiplied. In general, matrix multiplication is not commutative, and AB does not equal BA. However, there are certain special cases where AB=BA is true, such as when one of the matrices is the identity matrix or when the matrices commute with each other.
To determine if AB=BA is true for a specific set of matrices, you can simply perform the matrix multiplication and compare the results. If the two products are equal, then AB=BA is true. If they are not equal, then AB=BA is false.
The "Matrix: True or False? AB=BA" question has many real-world applications. In physics, it is used to calculate the moment of inertia of an object. In engineering, it is used in structural analysis and control systems. In computer science, it is used in graphics rendering and machine learning algorithms. Understanding the commutative property of matrix multiplication is essential in these fields to ensure accurate and efficient calculations.