1. ## Show that B=0

I would like some guidance on this question please:

Question:Consider A = $$\begin{pmatrix} 2 & -5 \\ 3 & 1 \end{pmatrix}$$
and let $$B= A^2 -3A+17I$ Show that B = 0 How do I begin answering a question like this? 2. Originally Posted by sparky I would like some guidance on this question please: Question:Consider A = $\[ \begin{pmatrix} 2 & -5 \\ 3 & 1 \end{pmatrix}$$
and let $$B= A^2 -3A+17I$ Show that B = 0 How do I begin answering a question like this? I hope you know how to multiply two matrices. Find $A^2=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}\times \begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}$ So, $B=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}^2-3\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}+17\begin{pmatrix}1 & 0 \\0 & 1\end{pmatrix}$ Hope you can continue. 3. Ok, I figured it out: B = $\[ \begin{pmatrix} 2 & -5 \\ 3 & 1 \end{pmatrix}$$
$$\begin{pmatrix} 2 & -5 \\ 3 & 1 \end{pmatrix}$$
- $$\begin{pmatrix} 6 & -15 \\ 9 & 3 \end{pmatrix}$$
+ $$\begin{pmatrix} 17 & 0 \\ 0 & 17 \end{pmatrix}$$

= $$\begin{pmatrix} -17 & 0 \\ 0 & -17 \end{pmatrix}$$
$$\begin{pmatrix} 17 & 0 \\ 0 & 17 \end{pmatrix}$$
= 0

I hope you know how to multiply two matrices. Find $A^2=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}\times \begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}$
So, $B=\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}^2-3\begin{pmatrix}2 & -5 \\3 & 1\end{pmatrix}+17\begin{pmatrix}1 & 0 \\0 & 1\end{pmatrix}$