If the matrix \(A = \begin{bmatrix} 0 & 2b & -2 \\ 3 & 1 & 3 \\ 3a & 3 & -1 \end{bmatrix}\) is symmetric, then the values of a and b are
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(a = -\displaystyle\frac{2}{3},\ b = \displaystyle\frac{3}{2}\)
In a symmetric matrix \(a_{ij} = a_{ji}\) for all i and j, so each element above the diagonal equals its mirror element below the diagonal.
Elements \(a_{12}\) and \(a_{21}\):
\(2b = 3\)
\( \displaystyle b = \frac{3}{2} \)
Elements \(a_{13}\) and \(a_{31}\):
\(3a = -2\)
\( \displaystyle a = -\frac{2}{3} \)
The last pair, \(a_{23} = 3\) and \(a_{32} = 3\), already agree.