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Question: find the order and inverse of each of the following...

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Find the order and inverse of each of the following:

Find the order and inverse of (4,7) in (Zs)* x (Z12)*. Also, what is the order of the group (Zs) x (Z12)? Note: (Zn) = U(Z.) = {z E Zn | gcd(z,n) = 1} (Gallian calls this U(n)) is the group of units of Zn. This is a group under multiplication modulo n. For example: (Z12)1,5,7,11). You should be multiplying. Find the order 3 9 in (Zio)2. Also, what is the order of the group (210)2*2? Note: (Zn)n×n is a group under (matrix) addition with entries added modulo m. You should be adding. Find the order and inverse of n 10 il l-acz.a).

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