3.5-34
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The result for dim(A)=3 is 

  A=diag(a,b,c) and A invertible if and only if abc is not zero.

The result for dim(A)= is 

  A=diag(a1,a2,...,an) and A invertible if and only if a1*a2*...*an is not zero.


You must present a proof for dim(A)=n. A dim(A)=3 proof earns 70% or less.

Resource: Theorem page 190, which says A is invertible if and only if rref(A)=I.

For dim(A)=3, the argument goes like this:


 I. If abc=0, then A has a row of zeros, hence rref(A) has a row of zeros
and then rref(A) is not the identity I. By page 190, A fails to be invertible.

 II. If abc is not zero then three multiply rules can be applied to reduce
matrix A to I, hence rref(A)=I. Page 190 implies A is invertible. 

 III. In case II, the inverse of A can be found by using the same three
mult rules on the augmented matrix C=aug(A,I) to give rref(C)=aug(I,B)
where B=diag(1/a,1/b,1/c).