Answer :

We are given that,


We need to find the value of A + AT.


We know that the transpose of a matrix is a new matrix whose rows are the columns of the original.


We have,



Here,


1st row of A = (1 2)


2nd row of A = (3 4)


Transpose of this matrix A, AT will be given as


1st column of AT = 1st row of A = (1 2)


2nd column of AT = 2nd row of A = (3 4)


Then,



For addition of two matrices, say X and Y, where



Add the corresponding elements of matrices X and Y.



Similarly, we need to add these two matrices, A and AT.



Adding the corresponding elements of the matrices A and AT,




Thus, we get the matrix .


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