Question

If
$\sf A \left[\begin{array}{ccc}1&4\\ 1&-3\\\end{array}\right] and \; B\left[\begin{array}{ccc}1&2\\-1 &-1\\\end{array}\right]$
then find
(A + B)²
A² + B²
Note
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Answer 1

Step-by-step explanation:

$\sf A=\left[\begin{array}{ccc}1&4 \\ 1&-3 \end{array} \right]$

$\\ \sf{:}\dashrightarrow A=1(-3)-1(4)$

$\\ \sf{:}\dashrightarrow A=-3-4$

$\\ \sf{:}\dashrightarrow A=-7$

______________________

$\sf B=\left[\begin{array}{ccc}1& 2\\ -1& -1 \end{array} \right]$

$\\ \sf{:}\dashrightarrow B=1(-1)-2(-1)$

$\\ \sf{:}\dashrightarrow B=-1-(-2)$

$\\ \sf{:}\dashrightarrow B=-1+2$

$\\ \sf{:}\dashrightarrow B=1$

now,

$\\ \sf{:}\dashrightarrow (A+B)^2$

$\\ \sf{:}\dashrightarrow A^2+2AB+B^2$

$\\ \sf{:}\dashrightarrow (-7)^2+2(-7)(1)+(1)^2$

$\\ \sf{:}\dashrightarrow 49+(-14)+1$

$\\ \sf{:}\dashrightarrow 49-14+1$

$\\ \sf{:}\dashrightarrow 35+1$

$\\ \sf{:}\dashrightarrow 36$

Again

$\\ \sf{:}\dashrightarrow A^2+B^2$

$\\ \sf{:}\dashrightarrow (A+B)^2-2AB$

$\\ \sf{:}\dashrightarrow 36-14$

$\\ \sf{:}\dashrightarrow 22$