Question

Show that $(A^t{)}^t=A$.

Short answer

We have proved that$(A^t{)}^t=A$.

Step-by-step solution

Step 1:

$A^t$represents the transpose of the matrix. It is obtained by interchanging rows and columns.

Step 2:

To proof: $(A^t{)}^t=A$

PROOF:

We can rewrite the matrix A as role="math" localid="1668442358509" $\left[a_{ij}\right]$where $a_{ij}$represents the element in the $i^{th}$row and $j^{th}$column of A.

The transposed matrix interchanges the rows and columns of the initial matrix.

$(A^t{)}^t=([a_{i}j{]}^t{)}^t=[a_{j}i{]}^t=\left[a_{i}j\right]=A$.