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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
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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