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Let $A$ be a $3\times 3$ matrix such that $\mid A-I \mid=0$.If trace of $A=13$ and $det A = 32$ then sum of squares of the eigen values of $A$ is .....

  1. $82$
  2. $13$
  3. $169$
  4. $81$
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|A-I|=0 it refers to or implies that one of the eigen value is 1 here. $\lambda 1 * \lambda 2 * \lambda 3$ = 32

$\lambda 1 + \lambda 2 +\lambda 3$ = 13  $\lambda 1 = 1$ therefore  $\lambda 2 + \lambda 3$ = 12

$\lambda 2* \lambda 3$=32

$\lambda  2$ =8

$\lambda 3 $ =4

1^(2) + 8^(2) + 4^(2) = 81
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