Right answer is (a) True
To explain I would say: The given statement is true.
Expanding the determinant Δ=\(\begin{vmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33} \end{vmatrix}\) along R1, we get
Δ=(-1)^1+1 a11 \(\begin{vmatrix}a_{22}&a_{23}\\a_{32}&a_{33} \end{vmatrix}\)+(-1)^1+2 a12 \(\begin{vmatrix}a_{21}&a_{23}\\a_{31}&a_{33} \end{vmatrix}\)+(-1)^1+3 a13 \(\begin{vmatrix}a_{21}&a_{22}\\a_{31}&a_{32} \end{vmatrix}\)
Δ=a11 A11+a21 A21+a31 A31, where Aij is the cofactor of aij.