If A = [(1,8),(4,3)] B = [(1,3),(7,4)] C = [(-4,6),(3,-5)] Prove that (i) AB ≠ BA

Question

If A = \(\begin{bmatrix} 1 & 8 \\[0.3em]4&3\end{bmatrix}\)B = \(\begin{bmatrix} 1 & 3 \\[0.3em]7&4\end{bmatrix}\) C = \(\begin{bmatrix} -4 & 6 \\[0.3em]3&-5\end{bmatrix}\)

Prove that 

(i) AB ≠ BA 

(ii) A(BC) = (AB)C 

(iii) A(B + C) = AB + AC 

(iv) AI = IA = A

Answer 1

(i) AB 

(ii) (AB)C

(iii) B + C 

(iv) Since order of A is 2 x 2, take