Question

If A is a matrix of order m x n then the order of $A^T$ where, $A^T$ is the transpose of A is

• A. m x n
• B. m x m
• C. n x m
• D. n x n

Answer 1

The correct option is C

n x m

Let $A=\left[\begin{array}{cc}{a}_1{a}_2.........n& elements\\ b_1{b}_2.........n& elements\\ melements& \end{array}\right]$ Every row has n elements i.e., number of columns = n. Every column has m elements i.e., number of rows = m.

Now if we take the transpose of this matrix then rows becomes columns and columns become rows.

So number of columns in the new matrix is the number of rows in the original matrix and number of rows in the new matrix is the number of columns in the original matrix.

So order changes from m $\times$ n to n $\times$ m on taking the transpose.