Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Recall that the function f:X to Y is invertible with inverse function g: Y to X if g(f(x))=x for all x in X and f(g(x))=x for all x in Y. Suppose T: R^n to^n is a matrix transformation defined by T(x)=A(x). Prove that if A is an invertible matrix then T is an invertible function.
Hint: Can you think of another matrix transformation that acts as the inverse for T?
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