If the \(2 \times 2\) matrix \(\mathbf{A}\) has an inverse and \((\mathbf{A} - 2 \mathbf{I})(\mathbf{A} - 4 \mathbf{I}) = \mathbf{0},\) then find \[\mathbf{A} + 8 \mathbf{A}^{-1}.\]
Like so:
Alternatively,
\(\displaystyle (A-2I)(A-4I)=A^{2}-6A+8I=0,\\ A^{2}+8I=6A,\\ A+8A^{-1}=6I.\)
Thanks Alan and guest.
I always need reminding about matrices :)
