First slide

Binomial theorem for positive integral Index

Question

$If A = {[a_{i j}]}_{4 \times 4}, such that a_{i j} = \{\begin{array}{l} 2, when i = j \\ 0, when i \neq j \end{array}, then \{\frac{det (adj (adj A))}{7}\} is (where {.} represents$ fractional part function)

Moderate

A

$\frac{1}{7}$
B

$\frac{2}{7}$
C

$\frac{3}{7}$
D

$\frac{4}{7}$

Solution

$From given data | A | = 2^{4}$
$\Rightarrow |a d j (a d j A)| = {(2^{4})}^{9} = 2^{36}$
$\Rightarrow \{\frac{\det (a d j (a d j A))}{7}\} = \{\frac{2^{36}}{7}\} = \{\frac{{(7 + 1)}^{12}}{7}\} = \frac{1}{7}$

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