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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices1 Mark
MCQ
If $A$ and $B$ are two matrices such that $AB = B$ and $BA = A, A^2 + B^2$ is equal to:
  • A
    $2AB$
  • B
    $2BA$
  • ✓
    $A + B$
  • D
    $AB$
✓

Answer

Correct option: C.
$A + B$
 Given $A B=A$ and $B A=B ,$ then 
$\Rightarrow \text{BAB}=B^2$ and $\text{ABA}=A^2$
$\Rightarrow B A=B^2$ and $A B=A^2$
$\Rightarrow B=B^2$ and $A=A^2$
$\Rightarrow A^2+B^2=A+B$

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