If $A = \ \begin{bmatrix} a + ib & c + id \ - c + id & a - ib \end{bmatrix}$ and $a^{2} + b^{2} + c^{2} + d^{2} = 1$, then $A^{- 1}$ is equal to

Question

Dr. Abubacker · Accepted Answer

(a)
We have,
$|A| = (a + ib)(a - ib)—c + id(c + id)$
$a^{2} + b^{2} + c^{2} + d^{2} = 1$
And adj$(A) = \begin{bmatrix}
a - ib & - c - id \
 - c - id & a + ib
\end{bmatrix}$
Then $A^{- 1} = \begin{bmatrix}
a - ib & - c - id \
 - c + id & a - ib
\end{bmatrix}$

Q. If $A = \ \begin{bmatrix} a + ib & c + id \\ - c + id & a - ib \end{bmatrix}$ and $a^{2} + b^{2} + c^{2} + d^{2} = 1$, then $A^{- 1}$ is equal to

Explanation

Reviewed by Dr. Abubacker

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