//Example 3.9
clc
clear

A = [1 1 1; 4 3 -1; 3 5 3];
n = length (A(1,:));
Aug = [A,eye(n,n)];

// Forward Elimination
for j = 1:n-1
    for i = j+1:n
        Aug(i,j:2*n) = Aug(i,j:2*n) - Aug(i,j) / Aug(j,j) * Aug(j,j:2*n);
    end
end

// Backward Elimination
for j = n:-1:2
    Aug(1:j-1,:) = Aug(1:j-1,:) - Aug(1:j-1,j) / Aug(j,j) * Aug(j,:);
end

// Diagonal Normalization
for j=1:n
    Aug(j,:) = Aug(j,:) / Aug(j,j);
end
Inv_A = Aug(:,n+1:2*n);
disp(Inv_A,"Inverse of A (A-1) = ")