If $A = \left\lbrack a_{ij} ight brack_{4 imes 4}$ , such that $a_{ij} = \begin{Bmatrix} 2, & when\ i = j \ 0, & when\ i\
eq j \end{Bmatrix}$, then $\left\{ \frac{det(adj(adj\ A))}{7} ight\}$ is (where {$\bullet$} represents fractional part function)

Question

If $A = \left\lbrack a_{ij} ightbrack_{4 	imes 4}$ , such that $a_{ij} = \begin{Bmatrix} 2, & when\ i = j \ 0, & when\ i\ 
eq j \end{Bmatrix}$, then $\left\{ \frac{det(adj(adj\ A))}{7} ight\}$ is (where {$\bullet$} represents fractional part function)

Dr. Abubacker · Accepted Answer

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

Q. If $A = \left\lbrack a_{ij} \right\rbrack_{4 \times 4}$ , such that $a_{ij} = \begin{Bmatrix} 2, & when\ i = j \\ 0, & when\ i\ \neq j \end{Bmatrix}$, then $\left\{ \frac{det(adj(adj\ A))}{7} \right\}$ is (where {$\bullet$} represents fractional part function)

Explanation

Reviewed by Dr. Abubacker

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