Question

$a = \begin{bmatrix} 8 & -3 \\ 4 & -1 end{bmatrix}$
what are the elements of the resulting matrix $a^2$
drag the numbers to the correct location in the matrix. not all numbers will be used.
$a^2 = \begin{bmatrix} & \\ & end{bmatrix}$
-27 -21 -13 -11 28 36 52 76

Explanation:

Step1: Define $A^2 = A \times A$

$A^2 =

$$\begin{bmatrix} 8 & -3 \\ 4 & -1 \end{bmatrix}$$

\times

$$\begin{bmatrix} 8 & -3 \\ 4 & -1 \end{bmatrix}$$

$

Step2: Calculate top-left element

$\text{Top-left} = (8 \times 8) + (-3 \times 4) = 64 - 12 = 52$

Step3: Calculate top-right element

$\text{Top-right} = (8 \times -3) + (-3 \times -1) = -24 + 3 = -21$

Step4: Calculate bottom-left element

$\text{Bottom-left} = (4 \times 8) + (-1 \times 4) = 32 - 4 = 28$

Step5: Calculate bottom-right element

$\text{Bottom-right} = (4 \times -3) + (-1 \times -1) = -12 + 1 = -11$

Answer:

$A^2 =

$$\begin{bmatrix} 52 & -21 \\ 28 & -11 \end{bmatrix}$$

$