Explanation:

Here’s what’s going on with these matrix statements:

- Statement 1: CA = CB

- Let’s check:

C is a column vector. A and B are 1×2 rows.

C * A is not defined (column × row here doesn’t work), unless you meant A * C and B * C (which would make sense, since those would be scalar results).

But as written, CA and CB are not defined. Call this one incorrect.

- Statement 2: AC = BC

- A and B are 1×2, C is 2×1. AC and BC are both 1×1 (scalars).

Calculating:

- AC = [m n][m, -m]^T = m*m + n*(-m)

- BC = [-n -m][m, -m]^T = (-n)*m + (-m)*(-m)

They’re not generally equal unless m = 0 or n = 0. This is also not guaranteed to be true.

- Statement 3: C(A+B) = CA + CB

- Matrix multiplication distributes over addition when defined.

- Let’s be careful with dimensions. C is 2×1, (A+B) is 1×2, so C(A+B) isn’t defined.

- So, this fails too.

Your actual options:

- Option 1: Statement 1 only

- Option 2: Statement 2 only

- Option 3: Statement 2 and 3

- Option 4: Statement 1 and 2