4. Consider the problem of matrix multiplication: Problem: Matrix Multiplication Input: Two matrices, A (of dimension x x y) and B (dimension y x 2). Output: An x x 2 matrix C, where C[i][j] is the dot product of the i-th row of A and the j-th column of B. The elementary algorithm for matrix multiplication is implemented as a tight product of three nested loops as follows: for (i = 1 to x) for (j = 1 to y) { C[i][j] = 0; for( k = 1 to z) { C[i][j] + + = } } A[i][k] * B[k][j]; } Consider C[i][j] ++ = A[i][k] * B[k][j] as the basic operation of matrix multiplication, please formally prove that, when x =y=2=n, the matrix multiplication algorithm is O(n). 4. Consider the problem of matrix multiplication: Problem: Matrix Multiplication Input: Two matrices, A (of dimension x x y) and B (dimension y x 2). Output: An x x 2 matrix C, where C[i][j] is the dot product of the i-th row of A and the j-th column of B. The elementary algorithm for matrix multiplication is implemented as a tight product of three nested loops as follows: for (i = 1 to x) for (j = 1 to y) { C[i][j] = 0; for( k = 1 to z) { C[i][j] + + = } } A[i][k] * B[k][j]; } Consider C[i][j] ++ = A[i][k] * B[k][j] as the basic operation of matrix multiplication, please formally prove that, when x =y=2=n, the matrix multiplication algorithm is O(n)