In the group GL(2,\mathbb{Z}_{7}), inverse of A-\left(\begin{array}{c}4&5\\ 6&3\end{array}\right) is ?

Umaiza Hutton

Umaiza Hutton

Answered question

2022-03-03

In the group GL(2,Z7), inverse of A(4563) is ?

Answer & Explanation

Riccardo Stewart

Riccardo Stewart

Beginner2022-03-04Added 3 answers

Soution: Group GL(2,Z7)
Find inverse of A=(4563)
for 2×2 matrix (abcd) then
(abcd)1=1adbc(dbca)
A=(4563)
|A|=4×36×5=1230=18
In 21718 is 3
|A|=3
(4563)1=13(3564)=31(3564)
13 in modulo 7 is 5
(4563)1=5(3564)
=5(3214)
=(1510520) (modulo 7)
(4563)1=(1356)

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