Show that if a is any m x n matrix, then ImA = A and AIn = A

  • Thread starter nietzsche
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  • #1
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Homework Statement



Show that if A is any m x n matrix, then the m x m identity multiplied by A = A, and A multiplied by the n x n identity = A.

Homework Equations





The Attempt at a Solution



I know how to prove this by writing out a general m x n matrix, and multiplying it by the identity, but is there a better way of showing this? It just seems kind of silly when I write it out...
 

Answers and Replies

  • #3
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I can`t really think of another way. The cleanest way I can think of:

[tex] (AI)_{i,j } = \sum_{r= 1}^n A_{i, r} I_{r, j} = a_{i, j} [/tex]
 

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