List of top Engineering Mathematics Questions on Determinants asked in TS PGECET

Let \(a,b\) and \(c\) be real numbers. Suppose there exist real numbers \(x,y,z\) which are not all zero such that the system of equations \(x = cy + bz\), \(y = cx + az\) and \(z = bx + ay\) has a non-zero solution then \(\left(a+b+c\right)^2 =\)

If $a = 2024$, $b = 2023$, and $c = 2022$, then the determinant \[ \begin{vmatrix} \log_a a & \log_a b & \log_a c \\ \log_b a & \log_b b & \log_b c \\ \log_c a & \log_c b & \log_c c \end{vmatrix} \] is: