I need help writing an creating an invertible matrix!!!!?

How about a 1 X 1 matrix with an element that is not -1, 1 or 0.

It will be invertible, and satisfy your requirements.

Additionally, if you want something that doesn't seem too 'cheap', use the observation that any invertible matrix has a non-zero determinant.

So, use a 2 X 2 matrix with the elements a, b, c, and d.

Let ab - cd = 0

Choose values for a, b, and c that are not -1, 1, or 0.

Solve for d, and voila, you get a matrix that satisfies your requirements.

Every non-zero 1x1 matrix is invertible. So, just give the matrix [10]. Its inverse is [1/10].

A 2x2 matrix

a b

c d

is invertible if and only if the "cross products" ad and bc are not equal. So, just stick random numbers in for a, b, c, and d, and compare their cross products. If they're equal, you're screwed (and amazingly unlucky). Just change one number, and it will be inverible. For example:

2 4

3 6

That doesn't invert, because 2 * 6 = 3 * 4. But if I change one number:

2 40

3 6

Now it's inverible.

a matrix will be invertible if it's determinant is non-zero. So, consider a 2 x 2 matrix with entries,

a b

c d

the determinant is ad - bc. So, as long as you make a, b, c, and d such that the determinant is not zero, you're good.

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the idea is to make it so that no column can be represented as a linear combination of other columns

[ 7 , 2 , 3

3, -2, 5

2, 7, 0 ]