5 1  Properties of transpose of the matrices
We now state the following properties of transpose of matrices without proof These
may be verified by taking suitable examples (i)For any matrices A and B of suitable orders, we have
(A′)′ = A,
(ii)
(kA)′ = kA′ (where k is any constant)
(iii)
(A + B)′ = A′ + B′
(iv)
(A B)′ = B′ A′
Example 20 If 
2
1
2
3
3
2
A
and B
1
2
4
4
2
0


−


=
=








, verify that
(i)
(A′)′ = A,
(ii)
(A + B)′ = A′ + B′,
(iii)
(kB)′ = kB′, where k is any constant