Let, show that, where I is the identity matrix of order 2 and n ∈ N

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Solution

It is given that

We shall prove the result by using the principle of mathematical induction.

For n = 1, we have:

Therefore, the result is true for n = 1.

Let the result be true for n = k.

That is,

Now, we prove that the result is true for n = k + 1.

Consider

From (1), we have:

Therefore, the result is true for n = k + 1.

Thus, by the principle of mathematical induction, we have:

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