Question

The adjoint of the matrix \[ A = \begin{pmatrix} 2 & 3
-3 & 5 \end{pmatrix} \] is

• A. \( \begin{pmatrix} 5 & 3
  -3 & 2 \end{pmatrix} \)
• B. \( \begin{pmatrix} 5 & -3
  3 & 2 \end{pmatrix} \)
• C. \( \frac{1}{19} \begin{pmatrix} 5 & -3
  -3 & 2 \end{pmatrix} \)
• D. \( \frac{1}{19} \begin{pmatrix} 5 & 3
  -3 & 2 \end{pmatrix} \)

Hint:

To find the adjoint of a 2x2 matrix, compute the cofactor matrix and take its transpose.

Answer 1

The Correct Option is A

Step 1: Formula for the adjoint of a matrix.
The adjoint of a matrix is the transpose of its cofactor matrix. The cofactor matrix of \( A \) is obtained by computing the minor matrix for each element and applying the appropriate sign. For the given matrix \( A \), the adjoint matrix is: \[ \text{Adj}(A) = \begin{pmatrix} 5 & 3
-3 & 2 \end{pmatrix} \]
Step 2: Conclusion.
Thus, the adjoint of the matrix is \( \begin{pmatrix} 5 & 3
-3 & 2 \end{pmatrix} \), corresponding to option (A).