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Inverse of a Matrix

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 $A^{- 1} =$

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Solution

$A = [\begin{matrix} a + i b & c + i d - c + i d & a - i b \end{matrix}]$
$A^{- 1} = \frac{Adj A}{| A |}$
$Adj A = [\begin{matrix} a - i b & - c - i d c - i d & a + i b \end{matrix}]$
$| A | = a^{2} + b^{2} + c^{2} + d^{2} = 1$
$\Rightarrow A^{- 1} = [\begin{matrix} a - i b & - c - i d c - i d & a + i b \end{matrix}]$

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Inverse of a Matrix

Standard XII Mathematics

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