If A = [ * 20 c a&b &a ] and A^2 = [ * 20 c & & ], then - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}a&b\\b&a\end{array}} \right]$ and ${A^2} = \left[ {\begin{array}{*{20}{c}}\alpha &\beta \\\beta &\alpha \end{array}} \right]$, then

A
$\alpha = {a^2} + {b^2},\beta = ab$
✓
$\alpha = {a^2} + {b^2},\beta = 2ab$
C
$\alpha = {a^2} + {b^2},\beta = {a^2} - {b^2}$
D
$\alpha = 2ab,\beta = {a^2} + {b^2}$

✓

Answer

Correct option: B.

$\alpha = {a^2} + {b^2},\beta = 2ab$

b
(b) ${A^2} = \left[ {\begin{array}{*{20}{c}}\alpha &\beta \\\beta &\alpha \end{array}} \right] = \left[ {\begin{array}{*{20}{c}}a&b\\b&a\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}a&b\\b&a\end{array}} \right]$; $\alpha = {a^2} + {b^2};\,\beta = 2ab.$

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