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STD 12 - 3 and 4 . determinant and metrices — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3 and 4 . determinant and metrices4 Marks
MCQ
If $A=\left(\begin{array}{ll}{2} & {2} \\ {9} & {4}\end{array}\right)$ and $I=\left(\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right),$ then $10 A^{-1}$ is equal to
  • A
    $4I-A$
  • ✓
    $A-6I$
  • C
    $6I-A$
  • D
    $A-4I$
✓

Answer

Correct option: B.
$A-6I$
b
$A=\left(\begin{array}{ll}{2} & {2} \\ {9} & {4}\end{array}\right) ;|A|=8-18=-10$

$A^{-1}=\frac{\operatorname{adj} A}{|A|}=\frac{\left(\begin{array}{cc}{4} & {-2} \\ {-9} & {2}\end{array}\right)}{-10}$

$10 \mathrm{A}^{-1}=\left(\begin{array}{cc}{-4} & {2} \\ {9} & {-2}\end{array}\right)=\mathrm{A}-6 \mathrm{I}$

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