Question

please answer to this ​

Answer 1

$\Large{\textsf{\textbf{ Question :-}}}$

if $\large\rm{ A = \left[ \begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array} \right] }$

and

$\large\rm{ B = \left[ \begin{array}{cc} 2 & 3 \\ 4 & 5 \end{array} \right] }$

then find

$\large\rm AB$

$\Large{\textsf{\textbf{ Answer :-}}}$

Given that,

$\large\rm{ A = \left[ \begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array} \right] }$ and $\large\rm{ B = \left[ \begin{array}{cc} 2 & 3 \\ 4 & 5 \end{array} \right] }$

$\large\rm$

$\scriptsize\rm{ = \left[ \begin{array}{cc} \rm a & \rm b \\ \rm c & \rm d \end{array} \right] \times \left[ \begin{array}{cc} \rm e & \rm f \\ \rm g & \rm h \end{array} \right] = \left[ \begin{array}{cc} \rm a \ast e + c \ast g & \rm a \ast f + c \ast h \\ \rm b \ast e + b \ast g & \rm b \ast f + d \ast h \end{array} \right] }$

$\large\rm$

$\large\rm{ = \left[ \begin{array}{cc} 1 \times 2 + 0 \times 4 & 1 \times 3 + 0 \times 4 \\ 0 \times 2 + 0 \times 4 & 0 \times 3 + 1 \times 5 \end{array} \right] }$

$\large\rm$

$\large\rm{ = \left[ \begin{array}{cc} 2+0 & 3+0 \\ 0+0 & 3+5 \end{array} \right]}$

$\large\rm$

$\large\rm{ = \left[ \begin{array}{cc} 2 & 3 \\ 0 & 5 \end{array} \right]}$

$\large\rm$

$\large\rm{ \:\:\:\:\:\;\:\:\;\:\:\: = (2)(5) - (3)(0)}$

$\large\rm$

$\large\rm{ \:\:\:\:\:\;\:\:\;\:\:\: = 10 - 0}$

$\large\rm$

$\large\rm{ \:\:\:\:\:\;\:\:\;\:\:\: = 10}$