Problem 1 30 points
In this problem we will test our basic knowledge of matrix multiplications, inverse and
transposes. Consider the following matrix A
A =

123
456
1. Write the expression for the transpose matrix AT
2. Compute A ⇥ AT and AT ⇥ A. Observe that you should see a symmetric matrix
3. Compute (A ⇥ AT )
1. Start with the augmented matrix [AAT |I] and use elementary
row operations to arrive at [I|(AAT )
1].
4. What happens when you try to do the same thing while calculating (AT A)
1. This
will not be invertible and you will arrive at an impasse. Don’t worry. Just show me