Statement (A): Adding the null matrix [ ll 0 & 0 0 & 0 ] to any 2… - Vidyadip

MCQ

Statement (A): Adding the null matrix $\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$ to any $2 \times 2$ matrix $\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$ will result in the original matrix $\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$.
Statement (B): Multiplying any $2 \times 2$ matrix by the identity matrix $\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ will change thevalues of the elements in the original matrix.
Which of the statement is valid?

✓
Only A
B
Only B
C
Both A and B
D
Neither A nor B

✓

Answer

Correct option: A.

Only A

(a) Only A
Explanation
For statement A,
If $\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]+\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$
Hence, adding the null matrix to any $2 \times 2$ matrix will result in the original matrix.
Statement A is correct.
For statement B,
If, $\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]=\left[\begin{array}{ll}a+0 & b+0 \\ 0+c & 0+d\end{array}\right]=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$
Hence, Multiplying any $2 \times 2$ matrix by the identity matrix $\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ will result in the original matrix.

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