MCQ
If $A$ and $ B$ are two square matrices such that $B = - {A^{ - 1}}BA$, then ${(A + B)^2} = $
- A$0$
- ✓${A^2} + {B^2}$
- C${A^2} + 2AB + {B^2}$
- D$A + B$
$\therefore$ $AB = - A{A^{ - 1}}BA = - IBA = - BA$
$\therefore$ $AB = - BA$
Now ${(A + B)^2} = (A + B)(A + B)$
= ${A^2} + AB + BA + {B^2}$
= ${A^2} + {B^2}$ [$\because$ $BA$= $-BA$]
Thus, ${(A + B)^2} = {A^2} + {B^2}.$
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