If A is a square matrix then,, A + A T is symmetric, AA T is skew - symmetric, A T + A is skew-symmetric, A T A is skew symmetric

Hints: ( A + A T ) T = A T + ( A T ) T = A T + A = A + A T

If A is a square matrix then,

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If $A$ is a square matrix then,

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Options:

A $\mathrm{A}+\mathrm{A}^{\mathrm{T}}$ is symmetric
B $\mathrm{AA}^{\mathrm{T}}$ is skew - symmetric
C $\mathrm{A}^{\mathrm{T}}+\mathrm{A}$ is skew-symmetric
D $\quad \mathrm{A}^{\mathrm{T}} \mathrm{A}$ is skew symmetric

Solution:

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The correct answer is: $\mathrm{A}+\mathrm{A}^{\mathrm{T}}$ is symmetric

Hints: $\left(\mathrm{A}+\mathrm{A}^{\mathrm{T}}\right)^{\mathrm{T}}=\mathrm{A}^{\mathrm{T}}+\left(\mathrm{A}^{\mathrm{T}}\right)^{\mathrm{T}}=\mathrm{A}^{\mathrm{T}}+\mathrm{A}=\mathrm{A}+\mathrm{A}^{\mathrm{T}}$

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