If possible, find A². (Note: A²= AA.) $A = \left[ \begin{array} { l l } 4 & 5 \ 4 & 4 \end{array} \right]$ A) $\left[ \begin{array} { l l } 34 & 40 \ 32 & 36 \end{array} \right]$ B) $\left[ \begin{array} { l l } 36 & 40 \ 32 & 36 \end{array} \right]$ C) $\left[ \begin{array} { l l } 32 & 40 \ 32 & 36 \end{array} \right]$ D) $\left[ \begin{array} { l l } 38 & 40 \ 32 & 36 \end{array} \right]$ E) $\left[ \begin{array} { l l } 40 & 40 \ 32 & 36 \end{array} \right]$

Question

Quizplus · Accepted Answer

Matrix multiplication of $A$ with itself (denoted as $AA$) involves multiplying the rows of the first matrix by the columns of the second matrix and summing the products. For the given matrix $A$, the calculation is as follows:- For the top-left element: $4*4 + 5*4 = 16 + 20 = 36$- For the top-right element: $4*5 + 5*4 = 20 + 20 = 40$- For the bottom-left element: $4*4 + 4*4 = 16 + 16 = 32$- For the bottom-right element: $4*5 + 4*4 = 20 + 16 = 36$Thus, the resulting matrix is $\left[ \begin{array} { l l } 36 & 40 \ 32 & 36 \end{array} \right]$, which matches option B.

If Possible, Find A2 A=[4544]A = \left[ \begin{array} { l l } 4 & 5 \\4 & 4\end{array} \right]A=[44​54​]

If Possible, Find A² $A = \left[ \begin{array} { l l } 4 & 5 \\4 & 4\end{array} \right]$