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Matrices and Determinants question

2024 · 29 Jan · Shift 1 · Q44

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JEE Main
Mathematics
Matrices and Determinants
2024 · 29 Jan · Shift 1 · Q44

Matrices and Determinants question

2024 · 29 Jan · Shift 1 · Q44

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

Let

\mathrm{A}

be a square matrix such that

\mathrm{AA}^{\mathrm{T}}=\mathrm{I}

. Then

\frac{1}{2} A\left[\left(A+A^T\right)^2+\left(A-A^T\right)^2\right]

is equal to

A
$\mathrm{A}^2+\mathrm{A}^{\mathrm{T}}$
B
$\mathrm{A}^3+\mathrm{I}$
C
$\mathrm{A}^3+\mathrm{A}^{\mathrm{T}}$
D
$\mathrm{A}^2+\mathrm{I}$

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