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by **Jbsmith11** on Mon Mar 28, 2011 4:02 pm

I need help with the following problems:

32. Find a formula for det (rA) when A is an n x n matrix and r is a scalar.

34. Let A and P be square matrices, with P invertible. Show that det [PA(P^-1)] = det A.

45. Suppose that all the entries in A are integers and det A = 1. Explain why all the entries in A^-1 are integers.

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by **Martingale** on Mon Mar 28, 2011 6:39 pm

Jbsmith11 wrote:I need help with the following problems:

32. Find a formula for det (rA) when A is an n x n matrix and r is a scalar.

34. Let A and P be square matrices, with P invertible. Show that det [PA(P^-1)] = det A.

45. Suppose that all the entries in A are integers and det A = 1. Explain why all the entries in A^-1 are integers.

$r^n$ now you figure out why.

Use: if $A,B$ are square matrices then $\det(AB)=\det(A)\det(B)$

use: $A^{-1}=\frac{1}{\det(A)}adj(A)$

by **Jbsmith11** on Tue Mar 29, 2011 2:46 am

Perfect, your hints really helped. I appreciate it.

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Help: properties of Determinants/cramer's rule section

Help: properties of Determinants/cramer's rule section

Re: Help: properties of Determinants/cramer's rule section

Re: Help: properties of Determinants/cramer's rule section