Assume P, Q, R and S are matrices of order 2 × m, k × n, m × 2 and 2 × 3 respectively. The restrictions on k, m and n, so that PQ + RS is defined are

m = 3, n = 2 m = n, k is arbitrary m = k, n is arbitrary m = k = 2, n = 3

m = k = 2, n = 3

order (P) = 2 × m     order (R) = m × 2 order (Q) = k × n order (S) = 2 × 3 for P × Q for R × S     m = k      2 = 2 order (P × Q) = 2 × n order (R × S) = m × 3 So for PQ+RS order (PQ) = order (RS) $2 × n=m × 3$ $n = 3, m = k = 2$