"Let $$A=\left(\begin{array}{cc}\mathrm{m} & \mathrm{n} \\ \mathrm{p} & \mathrm{q}\end{array}\right), \mathrm{d}=|\mathrm{A}| \neq 0$$ and $\mathrm{|A-d(A d j A)|=0}$. Then"

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$$\left| {A - d\left( {\matrix{ q & { - n} \cr { - p} & m \cr } } \right)} \right| = 0$$

$$\left| {\matrix{ {m - qd} & {n(1 + d)} \cr {p(1 + d)} & {q - md} \cr } } \right| = 0$$

$(m - qd)(q - md) = np{(1 + d)^2}$

$mq - ({q^2} + {m^2})d + qm{d^2} = np(1 + {d^2}) + 2npd$

${d^2}(mq - np) + 1(mq - np) = (2np + {m^2} + {q^2})d$

$({d^2} + 1)(mq - np) = (2np + m + a)d$

${d^2} + 1 = 2np + {m^2} + {q^2}$

$2d = 2mq - 2np$

$\Rightarrow {(1 + d)^2} = {(m + q)^2}$

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Let $$A=\left(\begin{array}{cc}\mathrm{m} & \mathrm{n} \\ \mathrm{p} & \mathrm{q}\end{array}\right), \mathrm{d}=|\mathrm{A}| \neq 0$$ and $\mathrm{|A-d(A d j A)|=0}$. Then

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Let $$A=\left(\begin{array}{cc}\mathrm{m} & \mathrm{n} \\ \mathrm{p} & \mathrm{q}\end{array}\right), \mathrm{d}=|\mathrm{A}| \neq 0$$ and $\mathrm{|A-d(A d j A)|=0}$. Then

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