Past exam of the mathematical methods I course of the University of Oxford / 2014 / 2

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- Solution 2

Solution

The determinant is

a^{2} - i (- i) = a^{2} - 1

. The adjugate matrix formula gives

A^{- 1} = \frac{1}{a ^{2} - 1} (a i - i a), a \neq = \pm 1.

When

a = 1

or

a = - 1

we have a singular matrix, so no inverse matrix exists. This criterion holds for real or complex

a

.

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