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Algebra of Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSAlgebra of Matrices1 Mark
MCQ
If $A$ and $B$ are two matrices such that $AB = A$ and $BA = B,$ then $B^2$ is equal to:
  • ✓
    $B$
  • B
    $A$
  • C
    $1$
  • D
    $0$
✓

Answer

Correct option: A.
$B$
Here, $AB = A ...(1)$
$BA = B ...(2)$
$\Rightarrow \text{BAB = BB} [$Multiplying both sides by $B]$
$\Rightarrow BA = B^2 [$From eq. $(1)]$
$\Rightarrow B = B^2 [$From eq. $(2)]$

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