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If $A$ is a square matrix, then what is adj $A^{T}-(a d j A)^{\mathrm{T}}$ equal to?
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The correct answer is:
Null Matrix
We know $\left(\operatorname{adj} \mathrm{A}^{\mathrm{T}}\right)=(\operatorname{adj} \mathrm{A})^{\mathrm{T}}$
$\Rightarrow\left(\operatorname{adj} \mathrm{A}^{\mathrm{T}}\right)-(\operatorname{adj} \mathrm{A})^{\mathrm{T}}=$ Null matrix
$\Rightarrow\left(\operatorname{adj} \mathrm{A}^{\mathrm{T}}\right)-(\operatorname{adj} \mathrm{A})^{\mathrm{T}}=$ Null matrix
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