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Assume other eigen value is $x$.

Sum of the eigen values is equal to the trace of the matrix.

​​​​​​$\implies 1+x=a+3$

Product of eigen values is equal to the determinant of the matrix.

$\implies x=3a-2$

Solving both equations, we get $a=2$

So $trace=a+3=5$

Answer is option (B).

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