Hi,
I would like some guidance on how to approach this question please:
Question: Let B be an n*n skew symmetric matrix and let A = I + B. Show that $\displaystyle AA^T = (I+B)(I-B)= A^TA$
Thanks for your reply Sambit.
I am still trying to figure out how you got $\displaystyle AA^T = (I + B)(I + B)^T$
Here is what I understand so far:
$\displaystyle B^T= -B$ (this is the definition of a skew symmetric matrix)
$\displaystyle A = I + B$ (this is given)
If $\displaystyle A = I + B$, then $\displaystyle A^T = -A = I - B$ (does this make any sense?)
Therefore, $\displaystyle AA^T = (I+B)(I-B)$ (is this correct?)