Could you please help me?

Dear Student,

A = |\begin{matrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{matrix}| Firstly we find the determinant of A as shown below : |A| = a [(a) (a) - (0) (0)] - 0 [(0) (a) - (0) (0)] + 0 [(0) (0) - (0) (a)] |A| = a [a^{2}] - 0 + 0 |A| = a^{3} Let C_{ij} be cofactor of a_{ij} in A . C_{11} = |\begin{matrix} a & 0 \\ 0 & a \end{matrix}| = a (a) - 0 (0) = a^{2} C_{12} = |\begin{matrix} 0 & 0 \\ 0 & a \end{matrix}| = 0 (a) - 0 (0) = 0 C_{13} = |\begin{matrix} 0 & a \\ 0 & 0 \end{matrix}| = 0 (0) - 0 (a) = 0 C_{13} = 0 Option (d) is correct

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