linear algebra 1

[laralina]

Hey, i am studying linear algebra 1 , i need a solution for this problem please , i don't know how to start

Let A =[aij] € GLn (IR) with aij element Z. Show the following statements:
1.) A^-1 element Qn,n
2.)A^-1 € Zn,n exactly when det(A) € {+1,-1}

 

[Steven G]

You need to have something to say about this problem. Can you state what A =[aij] means? How about GLn(|R)? And Qn,n?
Tutors on this forum do not give solutions for problems. Tutors only give hints to help the student get to the solution.
When a student claims that they do not know where to start, then we ask for definitions.

 

[pka]

Let A =[aij] € GLn (IR) with aij element Z. Show the following statements:
1.) A^-1 element Qn,n
2.)A^-1 € Zn,n exactly when det(A) € {+1,-1}

I second Jomo's comments. It may come a surprise to you but there is no standard in notation.
I for one taught linear algebra since the 1970's. But still I have no idea what the notation that you posted means.
I we are to be of help then you must tell us the notation means,

 

[HallsofIvy]

Hey, i am studying linear algebra 1 , i need a solution for this problem please , i don't know how to start

Let A =[aij] € GLn (IR) with aij element Z. Show the following statements:
1.) A^-1 element Qn,n
2.)A^-1 € Zn,n exactly when det(A) € {+1,-1}

This is poorly stated (perhaps English is not your native language?).
I would write "aij" with subscripts, \(\displaystyle a_{ij}\), or, if you can't use Latex, "a_{ij}". And \(\displaystyle a_{ij}\)are in Z. The multiplicative inverse (reciprocal) of an integer is NOT in general an integer but is 1 over that integer so is a rational number. The only integers who's reciprocal is an integer are 1 and -1.