If $| A | = K_{1}, | B | = K_{2}$ with $A B = I_{3}$ then evaluate ${(K_{1} K_{2})}^{2} + 2 K_{1} K_{2}$

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Solution

$A B = I$
$∣ A B ∣=∣ I ∣$
$K_{1} K_{2} = 1$
$(K_{1} K_{2})^{2} + 2 K_{1} K_{2} = 1 + 2 = 3$

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If |A|=K1,|B|=K2 with AB=I3 then evaluate (K1K2)2+2K1K2

AB=I∣AB∣=∣I∣K1K2=1(K1K2)2+2K1K2=1+2=3

If $| A | = K_{1}, | B | = K_{2}$ with $A B = I_{3}$ then evaluate ${(K_{1} K_{2})}^{2} + 2 K_{1} K_{2}$

$A B = I$
$∣ A B ∣=∣ I ∣$
$K_{1} K_{2} = 1$
$(K_{1} K_{2})^{2} + 2 K_{1} K_{2} = 1 + 2 = 3$