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**Please show work!!!**

Let $T:M(n,R)→M(n,R)$ be $T(A)=A−A_{T}$. Verify that $T$ is linear. What is the rank and nullity of the $T$ in the previous question? Explain your answer. (You may assume statements about dimensions of symmetric and antisymmetric matrices). Explain your answer.

Solution is shown below in detail

Linearity

Given that