Question

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disaproves the statement.

For any square matrices of the same siz, A(B+C)=AB+AC

Answer 1

True

Explanation:

Two matrices are equal if and only if:

(1)These matrices have the same dimensions.

(2) These matrices have equal corresponding elements.

Hypothesis says A,B,C are square matrices of the same size. Then condition (1) is satisfied.

For condition (2) is necessary to prove that each corresponding element is the same.

Check the image to read the proof.