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Let A, B, C be square matrices of equal orders and I be the identity matrix of same order, Then which of the following are TRUE?

A. (AB)C=A(BC)(AB)C = A(BC)

B. AB=BAAB = BA

C. A(B+C)=AB+ACA(B+C) = AB + AC

D. AI=IA=AAI = IA = A

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 2

Matrix multiplication is associative and distributive over addition, and II is the multiplicative identity, so A, C and D always hold.

Multiplication is not commutative in general, so B fails.

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