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# Let A=\begin{bmatrix}a&b\\c&d\end{bmatrix} and 'k' be the scalar. Find the formula that relates 'detKA' to 'K' and 'detA'' # Let A=\begin{bmatrix}a&b\\c&d\end{bmatrix} and 'k' be the scalar. Find the formula that relates 'detKA' to 'K' and 'detA''

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Vectors and spaces asked 2021-03-12

Let $$\displaystyle A=\begin{bmatrix}a&b\\c&d\end{bmatrix}$$ and 'k' be the scalar. Find the formula that relates 'detKA' to 'K' and 'detA''

## Answers (1) 2021-03-13

Given $$\displaystyle A=\begin{bmatrix}a&b\\c&d\end{bmatrix}$$
So $$\displaystyle kA=\begin{bmatrix}ka&kb\\kc&kd\end{bmatrix}$$
now $$\displaystyle det(kA)=\begin{vmatrix}ka&kb\\kc&kd\end{vmatrix}=k^2\begin{vmatrix}a & b \\c & d \end{vmatrix}$$
$$\displaystyle{\det{{\left({k}{A}\right)}}}={k}^{{2}}\ {\det{{\left({A}\right)}}}$$

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