Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Let A be a matrix that satisfies ?^2 =? where ? is the identity matrix.
a. Find a 2x2 example of such a matrix that is not

1 0
0 1

or

-1 0
0 -1


b. Prove that, in general (i.e, any size), any matrix that satisfies ?^2 =? must be invertible.

c. Explain why it must be the case that ?^−1 =?.

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