Let T be a linear operator on a finite-dimensional inner product space V. Prove the following results.

(a) N(T*) = N(T). Deduce that rank(T*T) = rank(T)

(b) rank(T) = rank(T*). Deduce from (a) that rank(TT*) = rank(T)

(c) For any nxn matrix A, rank(A*A) = rank(A)

PS: I'm not expecting you to try all of these. it's a super long problem so any hints will be greatly appreciated. so confused...sorry!!

thank you!