Assertion (A) : Scalar matrix A= [a_ i j ] = ll k ; & i=j 0 ; & i… - Vidyadip

MCQ

Assertion (A) : Scalar matrix $A=\left[a_{i j}\right]$ $=\left\{\begin{array}{ll}k ; & i=j \\ 0 ; & i \neq j\end{array}\right.$ where $k$ is a scalar, is an identity matrix when $k=1$.
Reason (R) : Every identity matrix is not a scalar matrix.

A
Both (A) and (R) are true and (R) is the correct explanation of (A).
B
Both (A) and (R) are true but (R) is not the correct explanation of (A).
✓
(A) is true but (R) is false.
D
(A) is false but (R) is true.

✓

Answer

Correct option: C.

(A) is true but (R) is false.

(c) : A scalar matrix $A=\left[a_{i j}\right]=\left\{\begin{array}{ll}k, & i=j \\ 0, & i \neq j\end{array}\right.$ is an identity matrix when $k=1$. But every identity matrix is clearly a scalar matrix.

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