1. The problem statement, all variables and given/known data If B=C^(-1) Is (B+C)^2=B^2+2BC+C^2 2. Relevant equations If A and B are (mXn) matrices and C is an (nXp) matrix, then (A+B)C=AC+BC If A is an mXn matrix and B and c are nXp matrices,then A(B+C)=AB+AC 3. The attempt at a solution (B+C)(B+C)=B^2+2BC+C^2 Then I decided to substitute B+C for D, but only one of them. D(B+C)=B^2+2BC+C^2 DB+DC=B^2+2BC+C^2 Then I substituted the b+c back in for D (B+C)B+(B+C)C=B^2+2BC+C^2 Then I get BB+CB+BC+CC=B^2+2BC+C^2 Then from here I plugged in the C^-1 in for the B's in the two middle terms, which gives c time c inverse, plust c inverse times C, and they both are equal to 1, and 1 plus 1 is equal to two so I get B^2+2+C^2=B^2+2BC+C^2 And then on the right hand side you can plug the c inverse in for b and you get 2 times c inverse times C which is just equal to 2. B^2+2+C^2=B^2+2+C^2 which finall gets me back to (B+C)^2=B^2+2BC+C^2 B^2+2+C^2=B^2+2+C^2 Did I screw up anywhere? The thing I am mainly not sure of is if I can make the substution like that.