Let A=Aij be an n×n operator matrix, where each Aij is a bounded linear operator on a complex Hilbert space. Among other numerical radius bounds, we show that w(A)≤w(A^), where A^=a^ij is an n×n complex matrix, with (Formula presented.) This is a considerable improvement of the existing bound w(A)≤w(A~), where A~=a~ij is an n×n complex matrix, with (Formula presented.) Further, applying the bounds, we develop the numerical radius bounds for the product of two operators and the commutator of operators. Also, we develop an upper bound for the spectral radius of the sum of the product of n pairs of operators, which improves the existing bound.