Let $A$ be a square matrix of order 3 such that $|A|=11$ and $B$ be the matrix of confactors of elements of $A$. Then, $|B|^{2}=$_________
Given:
$A$ be a square matrix of order 3
$|A|=11$
$B$ be the matrix of cofactors of elements of $A$
Since, $B$ be the matrix of cofactors of elements of $A$
$\Rightarrow B=(\operatorname{adj} A)^{T}$
$\Rightarrow|B|=\left|(\operatorname{adj} A)^{T}\right|$
$\Rightarrow|B|=|\operatorname{adj} A|$
$\Rightarrow|B|^{2}=|\operatorname{adj} A|^{2}$$\quad\left(\because\left|A^{T}\right|=|A|\right)$
As we know,
$|\operatorname{adj} A|=|A|^{n-1}$, where $n$ is the order of $A$
$\Rightarrow|B|=|A|^{n-1}$
$\Rightarrow|B|=|A|^{3-1} \quad(\because$ Order of $A$ is 3$)$
$\Rightarrow|B|=|A|^{2}$
$\Rightarrow|B|=(11)^{2} \quad(\because|A|=11)$
$\Rightarrow|B|=121$
$\Rightarrow|B|^{2}=(121)^{2}$
$\Rightarrow|B|^{2}=14641$
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