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If e ^(A) is difined as e ^(A) = I + A...

If `e ^(A)` is difined as
`e ^(A) = I + A + (A ^(2))/( 2 !) + .....` where
`= (1)/(2) [ {:(f (x), g (x)), (g (x), f (x)):}]`
`A = [{:(x,x),(x,x):}] and 0 lt x lt 1 ` is an identity matrix. Then `int _(0) ^(1) (g (x))/( f (x)) dx ` is equal

A

`ln ((e + e ^(-1))/( 2 ))`

B

`ln (e + e ^(-1))`

C

`ln (e ^(2) +1) - ln 2 `

D

None of these

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The correct Answer is:
A
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