Matrices and Determinants

JEE Main 2021 · 26 Aug, Morning shift · Q4504

MathematicsHard244×since 2002Q4504

A = \left( {\matrix{ {{1 \over {\sqrt 5 }}} & {{2 \over {\sqrt 5 }}} \cr {{{ - 2} \over {\sqrt 5 }}} & {{1 \over {\sqrt 5 }}} \cr } } \right)

B = \left( {\matrix{ 1 & 0 \cr i & 1 \cr } } \right)

i = \sqrt { - 1}

, and Q = A^TBA, then the inverse of the matrix A Q²⁰²¹ A^T is equal to :

JEE Main 2021 · 26 Aug, Morning shift · Q4504

MathematicsHard244×since 2002Q4504

A = \left( {\matrix{ {{1 \over {\sqrt 5 }}} & {{2 \over {\sqrt 5 }}} \cr {{{ - 2} \over {\sqrt 5 }}} & {{1 \over {\sqrt 5 }}} \cr } } \right)

B = \left( {\matrix{ 1 & 0 \cr i & 1 \cr } } \right)

i = \sqrt { - 1}

, and Q = A^TBA, then the inverse of the matrix A Q²⁰²¹ A^T is equal to :

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