For the covariance matrix show how we can get from step 1 to

For the covariance matrix, show how we can get from step 1 to step 2:

Solution

[x]ji means j rows and i colums

[x^-1]ij means i columns and j rows

the two matrix can be multiplied only if the number of rows of 1st is equal to the number of column of 2nd and the final dimensions of new matrix will be equal to the number of rows and column

here what we have is [x]ji[x^-1]ij here the number of rows of 1st matrix is j which is equal to the number of column i of 2nd and the resultand matrix have dimension of iXi

which means i rows and i column

now when the both will be multiplied we will get the step two = [xx^-1]ii