If A = [(3,5)(-2,0)(4,-6)] , verify that (2A)’ = 2A’.

Question

If A = \( \begin{bmatrix} 3 &5 \\[0.3em] -2 & 0 \\[0.3em] 4 &-6 \end{bmatrix},\) verify that (2A)’ = 2A’.

A = [(3,5)(-2,0)(4,-6)]

Answer 1

Given A = \( \begin{bmatrix} 3 &5 \\[0.3em] -2 & 0 \\[0.3em] 4 & -6 \end{bmatrix}\)

To Prove: (2A)’ = 2A’ 

Proof: Let us consider, B = 2A

Again to find RHS, we will find the transpose of matrix A

RHS = 2A’

LHS = RHS

Hence proved.