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3 and 4 .Determinants and Matrices
medium
Let $A =\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]$ and $B =\left[\begin{array}{l}\alpha \\ \beta\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0\end{array}\right]$ such that
$AB = B$ and $a + d =2021,$ then the value of $ad - bc$ is equal to ...... .
A
$1010$
B
$1560$
C
$2250$
D
$2020$
(JEE MAIN-2021)
Solution
$A =\left[\begin{array}{ll} a & b \\ c & d \end{array}\right], B =\left[\begin{array}{l}\alpha \\ \beta\end{array}\right]$
$AB = B$
$\Rightarrow( A – I ) B = O$
$\Rightarrow| A – I |= O ,$ since $B \neq O$
$\left|\begin{array}{cc}( a -1) & b \\ c & ( d -1)\end{array}\right|=0$
$ad – bc =2020$
Standard 12
Mathematics
