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Exercise 9.2.22. Suppose that (aod) e (boc) has an inverse in Z26: that is to say, suppose there is a ke Z26 such that k o ((a o d) e (bo c)) = 1. 9.2 PRIVATE KEY CRYPTOGRAPHY 275 Show that the matrices: A- (: :) kod -ko b -koc koa a b and B= ( are inverses of each other in Z26. That is, show that AB = BA = I under matrix multiplication mod 26.

Exercise 9.2.22. Suppose that (aod) e (boc) has an inverse in Z26: that is to say, suppose there is a ke Z26 such that k o ((a o d) e (bo c)) = 1. 9.2 PRIVATE KEY CRYPTOGRAPHY 275 Show that the matrices: A- (: :) kod -ko b -koc koa a b and B= ( are inverses of each other in Z26. That is, show that AB = BA = I under matrix multiplication mod 26.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 78E
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Exercise 9.2.22. Suppose that (aod) e (boc) has an inverse in Z26: that is to say, suppose there is a k e Z6 such that ko ((a o d) e (bo c)) = 1. 9.2 PRIVATE KEY CRYPTOGRAPHY 275 Show that the matrices: 4 - (: :) B - (* a kod -k o b A = and -k oc koa are inverses of each other in Z26. That is, show that AB = BA = I under matrix multiplication mod 26.
Transcribed Image Text:Exercise 9.2.22. Suppose that (aod) e (boc) has an inverse in Z26: that is to say, suppose there is a k e Z6 such that ko ((a o d) e (bo c)) = 1. 9.2 PRIVATE KEY CRYPTOGRAPHY 275 Show that the matrices: 4 - (: :) B - (* a kod -k o b A = and -k oc koa are inverses of each other in Z26. That is, show that AB = BA = I under matrix multiplication mod 26.
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