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  4. If A = [1&3 4&2] , B = [2&-1 1&2] , Then | ABB'| =

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Q. If $A = \begin{bmatrix}1&3\\ 4&2\end{bmatrix} , B = \begin{bmatrix}2&-1\\ 1&2\end{bmatrix} $ , Then | ABB'| =

KCETKCET 2019Matrices

Solution:

$A=\left[\begin{matrix}1&3\\ 4&2\end{matrix}\right] B=\left[\begin{matrix}2&-1\\ 1&2\end{matrix}\right] B'=\left[\begin{matrix}2&1\\ -1&2\end{matrix}\right]$
$\left|ABB'\right|=\left|A\right|\left|B\right|\left|B'\right|=\left(2-12\right)\times\left(4+1\right)\times\left(4+1\right)$
$=-10\times5\times5=-250$