Find A B if A = 6 9 2 3 and B = 2 6 0 7 9 8 .

Given, A = 6 9 2 3 and B = 2 6 0 7 9 8 AB is defined as the number of columns in matrix A is same as the number of rows in matrix B . Also AB is of order 2 × 3 . AB = 6 9 2 3 2 6 0 7 9 8 Applying row and column multiplication... AB = 6 × 2 + 9 × 7 6 × 6 + 9 × 9 6 × 0 + 9 × 8 2 × 2 + 3 × 7 2 × 6 + 3 × 9 2 × 0 + 3 × 8 AB = 12 + 63 36 + 81 0 + 72 4 + 21 12 + 27 0 + 24 AB = 75 117 72 25 39 24

If A = 3 3 2 4 2 0 , verify that A ' ' = A .

Given A = 3 3 2 4 2 0 The transpose of a matrix is found by interchanging its rows into columns or columns into rows. If A = a i j m × n , then A ' = a i j n × m Now A ' = 3 3 2 4 2 0 T = 3 4 3 2 2 0 A ' ' = 3 4 3 2 2 0 T = 3 3 2 4 2 0 So, A ' ' = 3 3 2 4 2 0 = A Hence A ' ' = A verified.