Two proving problem from the book Algebra by Artin

[GreenApple]

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

 

[Office_Shredder]

Probably.

It would help if we knew what the questions were. Where are you getting stuck exactly?

 

[GreenApple]

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