Shadow wrote:

aceminer wrote:

Let p be a prime. For every a ∈ Z, p, a^-1 ∈ Z

p is the unique element such that a × a^-1 mod p = 1. The operation ‘÷ mod p’ is defined as

(b = 1 ÷ a = (1/a) = a^-1 (mod p) ) ⇔ (b ∈ Zp ∧ b × a = a × b = 1 (mod p))

The Gauss-Jordan Algorithm can be adapted to compute the inverse of an invertible

matrix in modulo arithmetic over a prime modulus. Compute the following using

the (adapted) Gauss-Jordan Algorithm:

matrix A = ( 5 3 16

10 18 8

3 16 9 )

[(1/3) A^-1] mod 19

Could someone kindly explain to me what does this question exactly mean. I do not really understand it at all

You're trying to find a matrix

such that

Hint:

will simplify the number of calculations you need to do.

But how does the mod 19 come into play.

i am given the mapping of a to a^- 1 mod 19 values.

I am not sure how to even start. Do i reduce the matrix to its inverse form to find A^-1 first? but the inverse encompasses a such that

[(1/3)(A)]^-1.

Not too sure if 1/3 will play a part in this.