Question

If `A=[a_("ij")]_(4xx4)`, such that `a_("ij")={(2",","when "i=j),(0",","when "i ne j):}`, then `{("det (adj (adj A))")/(7)}` is (where `{*}` represents fractional part function)
A. `1//7`
B. `2//7`
C. `3//7`
D. none of these

Answer 1

Correct Answer - A
From given data, `|A|=2^(4)`
`implies |"adj. (adj. A)"|=(2^(4))^(9)=2^(36)`
`implies {("det. (adj. (adj. A)))/(7)}={2^(36)/7}={((7+1)^(12))/7}=1/7`