Answer each of the following as True or False justifying your answers: a.)If A and B are n×n matrices, then (A+B)²=A²+2AB+B².
b.)If A is an n×n invertible symmetric matrix, then (A⁻¹ )^k is symmetric, for any positive integer k.
c.)Let A be an n×n matrix. If A is invertible, then |A|≠0.
d.)If A and B are n×n matrices, then |A+B^T |=|A^T+B|.
e.)The vectors (a,0,0), (1,a,0) and (2,3,a) in R³ are linearly independent for all a∈R.