Find the matrix product when possible.
-Given $A = \left[ \begin{array} { r r } 5 & - 4 \ - 5 & 3 \end{array} \right]$, find $A ^ { 2 }$
A)
$$\left[ \begin{array} { r r }
45 & - 32 \
- 40 & 29
\end{array} \right]$$

B)
$\left[ \begin{array} { r r } 41 & - 37 \ 34 & - 5 \end{array} \right]$

C)
$\left[ \begin{array} { r r } 5 & - 8 \ - 10 & 11 \end{array} \right]$

D)
$\left[ \begin{array} { r r } 25 & 16 \ 25 & 9 \end{array} \right]$

Question

Find the matrix product when possible.
-Given $A = \left[ \begin{array} { r r } 5 & - 4 \ - 5 & 3 \end{array} \right]$, find $A ^ { 2 }$
A)
$$\left[ \begin{array} { r r } 
45 & - 32 \
- 40 & 29
\end{array} \right]$$

B)
$\left[ \begin{array} { r r } 41 & - 37 \ 34 & - 5 \end{array} \right]$

C)
$\left[ \begin{array} { r r } 5 & - 8 \ - 10 & 11 \end{array} \right]$

D)
$\left[ \begin{array} { r r } 25 & 16 \ 25 & 9 \end{array} \right]$

Quizplus · Accepted Answer

To find $A^2$, we multiply matrix $A$ by itself: $A \times A = \left[ \begin{array} { r r } 5 & - 4 \ - 5 & 3 \end{array} \right] \times \left[ \begin{array} { r r } 5 & - 4 \ - 5 & 3 \end{array} \right]$. The resulting matrix is $\left[ \begin{array} { r r } (5*5 + (-4)*(-5)) & (5*(-4) + (-4)*3) \ ((-5)*5 + 3*(-5)) & ((-5)*(-4) + 3*3) \end{array} \right] = \left[ \begin{array} { r r } 45 & - 32 \ - 40 & 29 \end{array} \right]$.

Find the Matrix Product When Possible A=[5−4−53]A = \left[ \begin{array} { r r } 5 & - 4 \\ - 5 & 3 \end{array} \right]A=[5−5​−43​]

Find the Matrix Product When Possible $A = \left[ \begin{array} { r r } 5 & - 4 \\ - 5 & 3 \end{array} \right]$