Find adjoint of each of the matrices : $\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$

Let $\left| {\begin{array}{*{20}{c}}
  {{{\left( {a – x} \right)}^2}}&{{{\left( {a – y} \right)}^2}}&{{{\left( {a – z} \right)}^2}} \\ 
  {{{\left( {b – x} \right)}^2}}&{{{\left( {b – y} \right)}^2}}&{{{\left( {b – z} \right)}^2}} \\ 
  {{{\left( {c – x} \right)}^2}}&{{{\left( {c – y} \right)}^2}}&{{{\left( {c – z} \right)}^2}} 
\end{array}} \right| = \frac{{ – 351}}{8}$ . If $x, y , z$ are the roots of the equation $8t^3 – 62t^2 + 43t -7 = 0$ and satisfy the determinant above, and $a, b, c$ are distinct number then value of $|(a – b) (b – c) (c – a)|$ is

Write Minors and Cofactors of the elements of following determinants: $\left|\begin{array}{ll}a & c \\ b & d\end{array}\right|$

Write Minors and Cofactors of the elements of following determinants : $\left|\begin{array}{rr}2 & -4 \\ 0 & 3\end{array}\right|$

Let ${\Delta _1} = \left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}\,} \right|$ and ${\Delta _2} = \left| {\,\begin{array}{*{20}{c}}{{\alpha _1}}&{{\beta _1}}&{{\gamma _1}}\\{{\alpha _2}}&{{\beta _2}}&{{\gamma _2}}\\{{\alpha _3}}&{{\beta _3}}&{{\gamma _3}}\end{array}\,} \right|$, then ${\Delta _1} \times {\Delta _2}$ can be expressed as the sum of how many determinants