Identify whether the following statements are true or false. If a statement is false, give an explanation why.
(a) An $n \times n$ matrix has $n$ eigenvalues.
(b) $\frac{6 - 12i}{2 + 3i} = 3 - 4i$
(c) If A is similar to the identity matrix, then det $A = 0$.
(d) If $x$ is an eigenvector of A, then the line through the origin and $x$ passes through $Ax$.
(e) If B and C are bases for the same vector space V, then B and C contain the same number of vectors.
(f) If $u$ and $v$ are in $\mathbb{R}^n$, then $u \cdot v = v \cdot u$.
(g) A is a diagonalizable matrix if $A = PDP^{-1}$ for some matrix D and some invertible matrix P.
