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(5) Recall That A Diagonal Matrix Is A Square Matrix Whose Only Nonzero Entries Lie On Its Diagonal.

(5) Recall that a diagonal matrix is a square matrix whose only nonzero entries lie on its diagonal. Computing powers of diagonal matrices is particularly nice because for p EN, OP X2 0 (i.e. raising a diagonal matrix to the power k is obtained by simply raising its diagonal entries to the power k.) Prove this property for any square matrix, and any exponent pe N, by using induction on p, and the componentwise definition of matrix multiplication. [3]