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Question 133

If $$i^2 = -1$$ and $$A = \begin{bmatrix}i & 0 \\0 & -i \end{bmatrix}$$ then $$A^{-1} =$$

Solution

As can be seen from the options, $$A^{-1}$$ is going to be a power of A itself.
We can continuing multiplying A successively to its own powers till we arrive at an identity matrix.
If the identity matrix is arrived at $$A^n$$ , then we can say that $$A^{n-1\ }=\ A^{-1}$$

Starting with the multiplication, we can see that a 2x2 identity matrix is arrived at at $$A^4$$
Hence, $$A^3$$ is the inverse of matrix A.

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