NIMCET 2023 Question Paper with solutions

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Question : 8 of 120

Marks: +1, -0

If

{\A}

and

{\B}

are square matrices such that

{\B}=- {\A}^{-1} {\BA}

, then

( {\A}+ {\B})^2=

${\A}^2+ {\B}^2$
${\A}^2- {\B}^2$
${\A}+ {\B}$
${\A}- {\B}$

Solution:

{\B}\;=- {\A}^{-1} {\BA}

{\AB}\;=- ( {\AA}^{-1}) {\BA}

{\AB}\;=- {\BA} ⇒ {\AB}+ {\BA}=0

∴ ( {\A}+ {\B})^2\;= {\A}^2+ {\B}^2+ {\AB}+ {\BA}

\;= {\A}^2+ {\B}^2 .

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