Consider the following statements in respect of square matrices A, B, C each of same order n :

1. AB = AC ⇒ B = C if A is non-singular

2. If BX = CX for every column matrix X having n rows then B = C

Which of the statements given above is/are correct ?  

The system of linear equations

x + 2y + z = 4, 2x + 4y + 2z = 8 and 3x + 6y + 3z = 10 has  

If A = $\left(\begin{array}{ccc}1 & 0 & 0 \\ 0 & \cos \theta & \sin \theta \\ 0 & \sin \theta & −\cos \theta\end{array}\right)$, then which of the following are correct?

1. A + adj A is a null matrix

2. A−1 + adj A is a null matrix

3. A − A−1 is a null matrix

Select the correct answer using the code given below :