# If the matrix X has a dimension of 4 times 6, matrix A has a dimension of 5 times 5, matrix

If the matrix X has a dimension of $4×6$, matrix A has a dimension of $5×5$, matrix B has a dimension of $3×5$ and matrix D has a dimension of $4×6$,The dimension of D' is $6×4$. True or false

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Step 1
According to the given information,
Consider the given dimension of the matrices.
$dim\left(X\right)=4×6$
$dim\left(A\right)=5×5$
$dim\left(B\right)=3×5$
$dim\left(D\right)=4×6$
Step 2
It is required to tell whether the dimension of D’ is $6×4$. D’ is the transpose of matrix and yes the dimension of D’ is $6×4$. So, the given statement is true.
example:
let $D={\left[\begin{array}{cccccc}1& 2& 3& 4& 5& 6\\ 1& 2& 3& 4& 5& 6\\ 1& 2& 3& 4& 5& 6\\ 1& 2& 4& 5& 6& 7\end{array}\right]}_{4×6}$
$D‘={\left[\begin{array}{cccc}1& 1& 1& 1\\ 2& 2& 2& 2\\ 3& 3& 3& 4\\ 4& 4& 4& 5\\ 5& 5& 5& 6\\ 6& 6& 6& 7\end{array}\right]}_{6×4}$