If a- b- c and d are real numbers such that a2 -b2- c2-d2-1 and if A- a-ib c-id- -c-id a-ib -where i2-1- then A-1-

A=[ a+ib amp; c+id; nbsp; c+id amp; a ib ] A^ 1=Adj A|A| Adj A=[ a ib amp; c id; nbsp; c id amp; a+ib ] |A|=a^2+b^2+c^2+d^2=1 ⇒ A^ 1= [ ...

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Sign of Quadratic Expression

If a, b, c an...

Question

If $a, b, c$ and $d$ are real numbers such that $a^{2} + b^{2} + c^{2} + d^{2} = 1$ and if $A = [\begin{matrix} a + i b & c + i d - c + i d & a - i b \end{matrix}],$ where $i^{2} = - 1,$ then $A^{- 1} =$

[\begin{matrix} a + i b & - c - i d c - i d & a - i b \end{matrix}]

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[\begin{matrix} a - i b & c + i d - c + i d & a + i b \end{matrix}]

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[\begin{matrix} a - i b & - c - i d c - i d & a + i b \end{matrix}]

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[\begin{matrix} a + i b & c + i d c - i d & a - i b \end{matrix}]

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a, b, c

d

a^{2} + b^{2} + c^{2} + d^{2} = 1

I f A = [\begin{matrix} a + i b & c + i d - c + i d & a - i b \end{matrix}]

A^{- 1} =

A = [\begin{matrix} a + i b & c + i d - c + i d & a - i b \end{matrix}]

a^{2} + b^{2} + c^{2} + d^{2} = 1

A^{- 1}

A = [\begin{matrix} a + i b & c + i d - c + i d & a - i b \end{matrix}]

a^{2} + b^{2} + c^{2} + d^{2} = 1

a, b, c

d

A = ∣ ∣ ∣ \begin{matrix} a + i b & c + i d - c + i d & a - i b \end{matrix} ∣ ∣ ∣

A^{- 1} =

(a + i b) (c + i d) = A + i B

(a^{2} + b^{2}) (c^{2} + d^{2}) = A^{2} + B^{2}

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