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## Homework Statement

If A is a an mxn matrix and its column vectors are linearly independent.

Prove that the matrix A

^{t}A is nonsingular. Hint: Use the fact that it is sufficient to show that null(A

^{t}A) = {0}

## Homework Equations

## The Attempt at a Solution

I'm new to this topic & I don't understand the hint given and how exactly to use it to prove the question...

I know that in order for a matrix to be nonsingular/invertible it has to be squre (m=n) and when you multiply the a matrix by its transpose, the resulting matrix would be square.

I'm also thinking about the properties of fundamental spaces of matrices that:

**row(A) = null(A)**and

**col(A)=null(A**(therefore null(A

^{t})^{t}A) = row(A).col(A)?)

Any help would be much appreciated :)

Cheers.