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In transpose of a matrix,
 Rows become columns and,

Column become rows
For matrix
It’s transpose is
We denote it by A’
Similarly for
Let’s look at some properties of transpose
Properties of transpose of a matrix
 (A’)’ = A
 (kA)’ = kA’
 (A + B)’ = A’ + B’
 (AB)’ = B’ A’
Let’s try to prove them one by one
Let
(A’)’ = A
Therefore,
(A’)’ = A
Therefore,
(4A)’ = 4A’
(A + B)’ = A’ + B’
(AB)’ = B’ A’
Therefore,
(AB)’ = B’ A’