Search any question & find its solution
Question:
Answered & Verified by Expert
If the matrix $A$ is both symmetric and skew symmetric, then
(a) $\mathbf{A}$ is a diagonal matrix
(b) $\mathbf{A}$ is a zero matrix
(c) $\mathbf{A}$ is a square matrix
(d) None of these
(a) $\mathbf{A}$ is a diagonal matrix
(b) $\mathbf{A}$ is a zero matrix
(c) $\mathbf{A}$ is a square matrix
(d) None of these
Solution:
2451 Upvotes
Verified Answer
$\mathrm{A}$ is a symmetric matrix if $\mathrm{a}_{\mathrm{ij}}=\mathrm{a}_{\mathrm{ji}} \mathrm{A}$ is a skew symmetric matrix if $\mathrm{a}_{\mathrm{ij}}=-\mathrm{a}_{\mathrm{ji}}$
$$
\text { If } a_{i j}=a_{j i}=-a_{j i} \Rightarrow a_{i j}=0
$$
$\Rightarrow \mathrm{A}$ is a zero matrix. Option (b) is correct.
$$
\text { If } a_{i j}=a_{j i}=-a_{j i} \Rightarrow a_{i j}=0
$$
$\Rightarrow \mathrm{A}$ is a zero matrix. Option (b) is correct.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.