Consider the following in respect of the matrices: A= [ array ll m & n array ], B= [ array ll -n & -m array ] and C= [ array c m -m array ] 1. C A=C B 2. A C=B C 3. C(A+B)=C A+C B Which of the above statements is/are correct?

Step-by-step solution

C A= [ array c m -m array ] [ array ll m & n array ]= [ array cc m^2 & m n -m^2 & -m n array ]C B= [ array c m -m array ][-n-m]= [ array cc -m n & -m^2 m n & m^2 array ] C A C B So, statement 1 is not correct. aligned & A C= [ array ll m & n array ] [ array c m -m array ]= [m^2-m n ] & B C= [ array ll -n & -m array ] [ array c m -m array ]= [-m n+m^2 ] aligned A C=B C So, statement 2 is correct. aligned & C(A+B)= [ array c m -m array ] [ array ll m-n & n-m array ] & = [ array cc m^2-m n & m n-m^2 -m^2+m n & -m n+m^