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Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics2 Marks
MCQ
If A and B are two square matrices such that $B=-A^{-1} B A$, then $(A+B)^2=$
  • A
    $0$
  • ✓
    $A ^2+ B ^2$
  • C
    $A^2+2 A B+B^2$
  • D
    $A+B$
✓

Answer

Correct option: B.
$A ^2+ B ^2$
(B) Given, $B =- A ^{-1} BA$
$\therefore \quad AB =- AA ^{-1} BA$
$\Rightarrow AB =- I ( BA ) \Rightarrow AB =- BA$
Now $(A+B)^2=(A+B)(A+B)$
$= A ^2+ AB + BA + B ^2$
$= A ^2+ B ^2 \quad[\because BA =- AB ]$

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