Question

If $A$ is a square matrix, then the value of $adj{A}^T-(adjA{)}^T$ is equal to

• A. $A$
• B. $2|A|I$, where $I$ is the identity matrix
• C. null matrix whose order is same as that of $A$
• D. unit matrix whose order is same as that of $A$

Answer 1

The correct option is C null matrix whose order is same as that of $A$

We know that the co factor matrix does not change for the matrix and its transpose,

$⟹adj{A}^T={\left(adjA\right)}^T⟹O$ where the null matrix has the same order of the matrix $A$