Question

If A = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`, Prove that (3A)^T = 3A^T 

Answer 1

A = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`

∴ A^T = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`

∴ 3A^T = `3[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`

= `[(3, 6, -15),(6, -9, 12),(-15, 12, 27)]`  ...(1)

3A = `3[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`

= `[(3, 6, -15),(6, -9, 12),(-15, 12, 27)]`

∴ (3A)^T = `[(3, 6, -15),(6, -9, 12),(-15, 12, 27)]`  ...(2)

From (1) and (2),

(3A)^T = 3A^T.