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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
If $A$ and $B$ are two matrices such that $AB = B$ and $BA = A,$ then ${A^2} + {B^2} = $
  • A
    $2AB$
  • B
    $2BA$
  • ✓
    $A + B$
  • D
    $AB$
✓

Answer

Correct option: C.
$A + B$
c
(c) We have $AB = B$ and $BA = A$.

Therefore ${A^2} + {B^2} = AA + BB = A(BA) + B(AB)$

$ = (AB)A + (BA)B = BA + AB = A + B$,

$(\because \,\,AB = B$ and $BA = A)$.

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