Question
The matrix $\left[ {\begin{array}{llllllllllllllllllll}1&0&0\\0&2&0\\0&0&4\end{array}} \right]$ is a
- (a) identity matrix
- (b) symmetric matrix ✓ Correct
- (c) skew-symmetric matrix
- (d) None of these
Matrices — Class 12 Maths Solution
Step-by-step Solution
Let $A = \left[ {\begin{array}{llllllllllllllllllll}1&0&0\\0&2&0\\0&0&4\end{array}} \right]$
$\therefore$ ${A^\prime } = \left[ {\begin{array}{llllllllllllllllllll}1&0&0\\0&2&0\\0&0&4\end{array}} \right] = A$
Therefore, the given matrix is a symmetric matrix.
[since, in a square matrix A, if ${A^\prime } = A$, then A is called symmetric matrix]
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Matrices. Curated by Sachin Sharma. Free for all students.