Sure, that's a good way to remember how the two matrices are related. In general, mathematicians like to use B' or B^T to name the transpose to make it even...
First, find the solutions x for det(A - xI) = 0, where I is the identity matrix and x is a variable. The solutions x are your eigenvalues. Let's say...
A scalar matrix is a square matrix that is a multiple of the identity matrix. In other words, the values on the main diagonal are all the same number, and...