1. Tardigrade
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  4. If A and B are non-singular matrices of order 3× 3, such that A=(adj B) and B=(adj A) , then det(A)+det(B) is equal to (where det(.M.) represents the determinant of matrix M and adjM represents the adjoint matrix of matrix M )

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Q. If $A$ and $B$ are non-singular matrices of order $3\times 3,$ such that $A=\left(adj B\right)$ and $B=\left(adj A\right)$ , then $det\left(A\right)+det\left(B\right)$ is equal to (where $det\left(\right.M\left.\right)$ represents the determinant of matrix $M$ and $adjM$ represents the adjoint matrix of matrix $M$ )

NTA AbhyasNTA Abhyas 2020Matrices

Solution:

$A=adjB=adj\left(adj A\right)=\left|A\right|A$
$\Rightarrow \left|A\right|=\left|A\right|^{4}\Rightarrow \left|A\right|=1\Rightarrow \left|B\right|=1$
Hence, $\left|A\right|+\left|B\right|=2$