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Invertible matrices

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Suppose that A and B are invertible n x n matrices

A. Show that if c ≠ 0, then cA is invertible. Justify your answer, using the definition of an invertible matrix.
What is (cA)-1 ?
B. Must A + B be invertible? If so, show that is it; if not give an example where it fails (and A and B are 2 x 2 or larger).


Solution Summary

This is a matrix theory problem that proves whether or not given matrices are invertible.