What about the definition of "commute"?Relevant equations None.
Jamin2112 said:Figured out the answer, I think. The sum of every row and column is the same.
Dick said:Sounds right, can you prove it?
Jamin2112 said:Yes, but the problem doesn't ask me to
A matrix that commutes with a matrix of ones is a square matrix that, when multiplied with a matrix of ones, gives the same result regardless of the order in which the multiplication is performed.
To determine which matrices commute with a matrix of ones, you can use the commutativity property, which states that two matrices A and B commute if and only if AB = BA. In other words, if the product of a matrix with a matrix of ones is equal to the product of a matrix of ones with the matrix, then the matrix commutes with the matrix of ones.
No, not all matrices can commute with a matrix of ones. For example, a matrix with only zeros in its entries will not commute with a matrix of ones because the product of the two matrices will always result in a matrix of zeros, which is not equal to the original matrix of ones.
One special property of matrices that commute with a matrix of ones is that they are diagonalizable. This means that they can be written in the form of a diagonal matrix, which can make certain calculations and operations easier to perform.
If two matrices commute with each other, they are said to be linearly independent. This means that they cannot be written as a linear combination of each other, and they have unique properties that make them useful in various mathematical and scientific applications.