Two proving problem from the book Algebra by Artin

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Can anyone give me some hint on proving 1.3 13 and 1.5 3 of Algebra by Artin?
 
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Probably.

It would help if we knew what the questions were. Where are you getting stuck exactly?
 
the first problem : M is a 2n*2n matrix in the form A B C D where each block A(at the position 1,1) B(1,2) C(2,1) D(2,2) is an n*n block. A is invertible and AC=CA. Prove the det M = det (AD - CB)

the second problem:
A is an n*n matrix with integer entries. Prove that the inverse of A has integer entries if and only if det A = 1 or -1
 
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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