Let A = [ ll a & b c & d ] and B = [ l ] [ l 0 0 ] such that AB =… - Vidyadip

MCQ

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
$2250$
✓
$2020$

✓

Answer

Correct option: D.

$2020$

$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 $B \neq O$
$\left|\begin{array}{cc}( a -1) & b \\ c & ( d -1)\end{array}\right|=0$
$ad - bc =2020$

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