Question

if X=AB+BA and Y=AB-BA then find XY whole transpose​

Answer 1

Answer:

XY = ( AB + BA ) ( AB - BA )

here , using identity ( a+b) (a-b) = a² - b²

XY = ( AB )² - ( XY )²

hope it helps ✔✔

Answer 2

AnswEr:

$\normalsize\bullet\:\sf\ X = (AB + BA)$

$\normalsize\bullet\:\sf\ Y = (AB - BA)$

We have to find the value of XY (i.e. X × Y).Block the values of X and Y to find XY.

Let's Begin!

$\rule{170}2$

$\underline{\bigstar\:\textsf{Value \: of \: XY:-}}$

$\normalsize\dashrightarrow\quad\sf\ XY = X \times\ Y$

$\normalsize\dashrightarrow\quad\sf\ XY = (AB + BA) \times\ (AB - BA)$

$\scriptsize\sf{\qquad\dag\ (a+b)(a-b) = a^2 - b^2}$

$\normalsize\dashrightarrow\quad\sf\ XY = (AB)^2 - (BA)^2$

$\normalsize\dashrightarrow\quad\sf\ XY = AB^2 - BA^2$

$\normalsize\dashrightarrow\quad{\underline{\boxed{\sf \red{ XY = AB^2 - BA^2}}}}$

$\rule{100}1$

$\boxed{\begin{minipage}{6 cm}\bf{\dag}\:\:\underline{\text{Important Algebric Identities :}}\\\\\bigstar\:\:\sf(a+b)^2 = a^2 + b^2 +2ab\\\\\bigstar\:\:\sf(a - b)^2 = a^2 + b^2 - 2ab\\\\\bigstar\:\:\sf(a+b)(a-b) = a^2 - b^2\\\\\bigstar\:\:\sf(a + b)^3 = a^3 + b^3 + 3ab(a + b)\\\\\bigstar\:\:\sf(a-b)^3 = a^3 - b^3 - 3ab(a - b)\\\\\bigstar\:\:\sf(a^3 - b^3) = (a - b) (a^2 + ab + b^2)\\\\\bigstar\:\:\sf(a^3 + b^3) = (a+b)(a^2 - ab + b^2)\end{minipage}}$