Question

Find each matrix below. If a matrix is not defined, click on "Undefined".(b)BA (c)B²

Answer 1

Given the matrices A and B below:

`$A=\mleft[\begin{array}{cc}2 & 0 \\ -3 & 3\end{array}\mright]$,$B=\mleft[\begin{array}{cc}-1 & -3 \\ 0 & 2\end{array}\mright]$`

Part B

`\begin{gathered} BA=\mleft[\begin{array}{cc}-1 & -3 \\ 0 & 2\end{array}\mright]\mleft[\begin{array}{cc}2 & 0 \\ -3 & 3\end{array}\mright] \\ $=\mleft[\begin{array}{cc}(-1*2)+(-3*-3) & (-1*0)+(-3*3) \\ (0*2)+(2*-3) & (0*0)+(2*3)\end{array}\mright]$ \\ $=\mleft[\begin{array}{cc}-2+9 & 0-9 \\ 0-6 & 0+6\end{array}\mright]$ \\ $BA=\lbrack\begin{array}{cc}7 & -9 \\ -6 & 6\end{array}\rbrack$ \end{gathered}`

Part C

`\begin{gathered} $B=\mleft[\begin{array}{cc}-1 & -3 \\ 0 & 2\end{array}\mright]$ \\ \implies B^2=\mleft[\begin{array}{cc}-1 & -3 \\ 0 & 2\end{array}\mright]\mleft[\begin{array}{cc}-1 & -3 \\ 0 & 2\end{array}\mright] \\ =\mleft[\begin{array}{cc}(-1*-1)+(-3*0) & (-1*-3)+(-3*2) \\ (0*-1)+(2*0) & (0*-3)+(2*2)\end{array}\mright] \\ =\mleft[\begin{array}{cc}1+0 & 3-6 \\ 0+0 & 0+4\end{array}\mright] \\ \implies B^2=\mleft[\begin{array}{cc}1 & -3 \\ 0 & 4\end{array}\mright] \end{gathered}`