Please Do 5 Show that if A is nonsingular then AAT is also n

Please Do #5

Show that if A is nonsingular, then AA^T is also nonsingular. Be sum to include enough words of explanation. What does it mean to say that (x, y) is an inner product? State as much of the definition as you can remember. It has 3 main parts. Suppose A is a nonsingular 4 times 4 matrix. Show that (x, y) = (Ax) - (Ay) is an inner product on R^4 (the dot in the formula is the usual dot product). Use greaterthanorequalto to get A into RREF; A = {i 1 i 1 0 2}

Solution

If A is non singular then

detA not equal to zero

So transpose of A is also

non singular matrix

Any two non singular matrices

multiplication is also non singular

So AA^T is also non singular matrix