Can AB^2009 be calculated?Matrix Multiplication and Exponentiation Limitations

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Homework Help Overview

The discussion revolves around the multiplication and exponentiation of square matrices, specifically the expression AB^2009. Participants are exploring the feasibility of calculating this expression given the properties of matrix multiplication.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster questions the possibility of computing AB^2009 and expresses uncertainty about the implications of the exponent on matrix multiplication. Other participants discuss the dimensions of the resulting matrices when multiplying A and B, and whether the exponent affects the outcome.

Discussion Status

The discussion is active, with participants exploring different interpretations of the expression and clarifying the properties of matrix multiplication. Some guidance is offered regarding the dimensions of the matrices involved, but there is no explicit consensus on the original poster's question.

Contextual Notes

The original poster mentions a constraint from an exam setting where calculators were not allowed, which may influence their understanding of the problem. There is also a question about the notation used in the expression, indicating potential ambiguity in interpretation.

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Homework Statement



Matrix A and B are both square matrices of the same size.

Is it possible to compute,

AB^2009

If not, why not?

The Attempt at a Solution



Just had this question in an exam, the exam did not allow calculators and I could not answer this question, I gather it is not possible but I cannot explain why.

Because A and B are square matrices it is possible to multiply them together but I am unsure about the exponent. Any ideas?
 
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Suppose that A and B are both n x n matrices. Then what is the size of AB? Then what about ABB = AB^2? And ABBB = AB^3? ...
 
Well if A and B are both n x n then they will always be n x n matrices. So does that mean that it is possible?
 
By the way, is that AB2009[/b] or (AB)2009?

It doesn' really matter. The only important point is that any two n by n matrices can be multiplied and give an n by n matrix as a result- which can be multiplied again by any other n by n matrix.
 

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