Question

If A is $2\times 2$ matrix, $detA=4$ then find the product of $det\left(3A\right)$ and $det\left(A^{-1}\right)$

Answer 1

Given $A$ is $2\times 2$ matrix,$\left|A\right|$

i) det(3A)

using properties of determinat

$\left|KA\right|=K^n\left|A\right|,n=$ order of determinant

$det\left(3A\right)=3^2\left|A\right|det\left(3A\right)=9\times 4=36ii\left)det\right(A^{-1})$

using properties of determinant

$det\left(A^{-1}\right)=\frac{1}{det\left(A\right)}=\frac{1}{4}.$