How to do (a + b)^2 for matrices?

[zoh]

Hi,
for integers, if we have (a + b)^2 , we can simply expand (a^2 + b^2 + 2*a*b).
but if 'a' and 'b' are matrices such that 'a' is of size 3*N and 'b' is of size N*3, is it the same rule ?

for the a^2 and b^2 parts, we simply multiply by their transposes. but do we have the right to do the last part like for integers i.e. 2*a*b ? or is there altogether a different way of doing (a + b)^2 for matrices ?

thanx in advance,

 

[daon2]

1. a+b only makes sense if a and b are the same size.
2. the square of a matrix only makes sense, oddly enough, if the matrix is square.

If the matrices are appropriately sized (guess what sizes they can be), then use your FOIL technique to determine what (a+b)^2 must be. Note that a*b and b*a are not necessarily the same.