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Sasor
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Homework Statement
If A is a matrix, find B, a matrix so that
AB=BA
Homework Equations
?
The Attempt at a Solution
Solve for inverse?
Sasor said:Homework Statement
If A is a matrix, find B, a matrix so that
AB=BA
Homework Equations
?
The Attempt at a Solution
Solve for inverse?
This statement can be made true by ensuring that the matrices A and B are both square matrices of the same dimension. Additionally, the order of multiplication should be considered, as changing the order can change the result.
In mathematics, matrices are used to represent linear transformations. If AB and BA are not equal, it means that the order of operations affects the result, which can have significant implications in certain applications such as computer graphics and data analysis.
The equal sign in this statement signifies that the two matrices are equal in terms of their resulting values after multiplication. It also indicates that the matrices are commutative, meaning the order of multiplication does not affect the result.
One example of matrices that satisfy this statement is:
A = [5 2; 3 1] and B = [4 1; 2 3]
When multiplied, AB and BA both result in the matrix:
[22 13; 14 8]
Yes, there are certain special cases where this statement may not hold true. For example, if either A or B is a non-square matrix, the statement will not hold. Additionally, if the matrices are not of the same dimension, the statement will not be valid. Finally, if the matrices have complex elements, the statement may not be true due to the non-commutativity of complex numbers.