According to the calculation form of,,, it is assumed first, and then proved by mathematical induction: if, the equation is obviously established; Assuming that the equation holds, it can be deduced from the matrix multiplication rule that the equation also holds at that time, from which it can be concluded that the original equation holds for any positive integer.
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Proof: guess (points)
When we clearly know.
The hypothesis holds.
Then at that time, there was a definition.
Also established.
Therefore, we can see that it is correct for anything.
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This question takes the second-order determinant as the carrier and examines the general steps of mathematical induction, which belongs to the intermediate question. It is the key to solve this problem to remember the multiplication rule of second-order matrix and use it accurately.