Define what it means for two $n \times n$ matrices $A$ and $B$ to be similar. Define the Jordan normal form of a matrix.

Determine whether the matrices

$$A=\left(\begin{array}{ccc} 4 & 6 & -15 \\ 1 & 3 & -5 \\ 1 & 2 & -4 \end{array}\right), \quad B=\left(\begin{array}{ccc} 1 & -3 & 3 \\ -2 & -6 & 13 \\ -1 & -4 & 8 \end{array}\right)$$

are similar, carefully stating any theorem you use.