 Hi and welcome to the last session where this class is following question. The question says it makes us equal to this matrix, prove that x to the power n is equal to this matrix where n belongs to natural numbers. Let's now begin with this solution. We shall prove this by mathematical induction on n. x to the power n is equal to cos nothing but the matrix x itself. So we can say that the result is true for x to the power m is equal to x to the power m is equal to sin mA into sin A into sin A sorry where we will prove to m plus 1 it is true for n equals to n. Hence by principle of mathematical induction it deserves as value virtual numbers. Thanks for watching.