Hi

I want to prove

(ab)AB = (aA)(bB), in which a, b E R and matrix multiplication AB are defined.

Proof.

Let A =(r_ij), B = (s_ij)

(aA + bB)

= ((a * r_ij) + (b * s_ij))

= (a * r_ij + b * s_ij)

= (a * r_ji + b * s_ji)

= (a * r_ji) + (b * s_ji)

= aA + bB

But I don't know are there errors in a proof. ?