Linear Algebra Question: Matrix multiplied by a column of its inverse

[DrexelDan]

X is a 10x10 matrix

what is X*[7th column of X's inverse]?

thanks for any help you can provide!

 

[DrexelDan]

I'm sure that I can just make a matrix up then find its inverse and multiply the original by the 7th column of the inverse but is there a general rule for doing this?

 

[DrexelDan]

I also know that a matrix multiplied by its inverse is the identity matrix. would the resultant matrix of the problem above be: in one column [0 0 0 0 0 0 1 0 0 0]

 

[Dick]

I also know that a matrix multiplied by its inverse is the identity matrix. would the resultant matrix of the problem above be: in one column [0 0 0 0 0 0 1 0 0 0]

You've got it.

 

[DrexelDan]

Thanks!