For a k-by-k matrix M, the matrix Mn is also k-by-k, and its value is the result of the n-fold multiplication of M by itself: MM M. Or we can define matrix exponentiation recursively: M0 := I (the...

For a k-by-k matrix M, the matrix Mn is also k-by-k, and its value is the result of the n-fold multiplication of M by itself: MM M. Or we can define matrix exponentiation recursively: M⁰
:= I (the k-by-k identity matrix), and Mⁿ+1 := M Mⁿ
. With this definition in mind, prove the following identity: