Easy
Write the minors and cofactors of the elements of the following determinant: $\left|\begin{array}{ll}a & c \\ b & d\end{array}\right|$
The given determinant is $\left|\begin{array}{ll}a & c \\ b & d\end{array}\right|$.
The minor of an element $a_{ij}$ is denoted by $M_{ij}$.
$M_{11} = \text{minor of element } a_{11} = d$
$M_{12} = \text{minor of element } a_{12} = b$
$M_{21} = \text{minor of element } a_{21} = c$
$M_{22} = \text{minor of element } a_{22} = a$
The cofactor of an element $a_{ij}$ is denoted by $A_{ij} = (-1)^{i+j} M_{ij}$.
$A_{11} = (-1)^{1+1} M_{11} = (-1)^{2}(d) = d$
$A_{12} = (-1)^{1+2} M_{12} = (-1)^{3}(b) = -b$
$A_{21} = (-1)^{2+1} M_{21} = (-1)^{3}(c) = -c$
$A_{22} = (-1)^{2+2} M_{22} = (-1)^{4}(a) = a$
The minor of an element $a_{ij}$ is denoted by $M_{ij}$.
$M_{11} = \text{minor of element } a_{11} = d$
$M_{12} = \text{minor of element } a_{12} = b$
$M_{21} = \text{minor of element } a_{21} = c$
$M_{22} = \text{minor of element } a_{22} = a$
The cofactor of an element $a_{ij}$ is denoted by $A_{ij} = (-1)^{i+j} M_{ij}$.
$A_{11} = (-1)^{1+1} M_{11} = (-1)^{2}(d) = d$
$A_{12} = (-1)^{1+2} M_{12} = (-1)^{3}(b) = -b$
$A_{21} = (-1)^{2+1} M_{21} = (-1)^{3}(c) = -c$
$A_{22} = (-1)^{2+2} M_{22} = (-1)^{4}(a) = a$
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