a. If exists, then exists.

Always.

If exists, and have the same dimensions.

If and have the same dimensions,then exists.

b.

If is a real number, then and exist.

Always.

If is a real number, then by the definition of scalar multiplication,

For exampl,

and .

c.

If does not exist, then does not exist.

Always.

If does not exist, then and must have different dimensions.

If and have different dimensions, then does not exist.

d.

If and have the same number of elements, then exists.

Sometimes.

Matrices must have the same dimensions for their sum to exist.

e.

If exists and exists, then exists.

Sometimes; matrices must have the same dimensions for their sum to exist.

a. Always.

b. Always.

c. Always.

d. Sometimes.

e. Sometimes.