The matrix $A = \begin{bmatrix} -4 & -3 & -3 \\ 1 & 0 & 1 \\ 4 & 4 & x \end{bmatrix}$ is its own adjoint. The value of x will be
- A. 5
- B. 3
- C. -3
- D. -5
Answer: B. 3
Explanation: If $A = adj(A)$, then $A_{11} = C_{11}$, etc. $C_{33} = (-4)(0) - (-3)(1) = 3$. Since $A_{33} = x$, then $x=3$.