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How can I prove that a function which takes an nxn matrix and returns that matrix cubed is a continuous function? Also, how can I analyze if the function is differenciable or not?

About the continuity I took a generic matrix A and considered the matrix A + h, where h is a real tending to zero. Then I generalized the product of two matrices A and B where the result is a matrix with a sum in each entry. Then the result of the product of the matrices A+h and B+h is a matrix like A.B plus some constants tending to zero. Although I'm not sure that's enough to prove the continuity.

Any help with this and the differenciation?

Thanks!

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# Function over matrices, continuous and differentiable?

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