Question

Decrypt the received encoded message [2 – 3][20 – 4] with the encryption matrix `[(-1, -1),(2, 1)]` and the decryption matrix as its inverse, where the system of codes are described by the numbers 1 – 26 to the letters A – Z respectively, and the number 0 to a blank space

Answer 1

Let the encoding matrix A = `[(-1, -1),(2, 1)]`

Given the encoded message is  [2 – 3][20 – 4]

|A| = – 1 + 2

= 1 ≠ 0.A^–1 exists.

adj A = `[(1, 1),(-2, -1)]`

A^–1 = `1/|"A"|` adj A = `[(1, 1),(-2, -1)]`

The receiver decodes the coded message as follows:

Codes row Matrix	Decoding matrix	Decoded row matrix
[2 – 3]	`[(1, 1),(-2, -1)]`	= `[(2 + 6, 2 + 3)]`
[20 –  4]	`[(1, 1),(-2, -1)]`	= `[(20 - 8, 20 - 4)]` = `[(12, 16)]`

So the sequence of decoded row matrics is [8 5][12 16]

The receiver reads the message as “HELP”.