Match List I with List II
| LIST I | LIST II | ||
| A. | $A+A^T$ | I. | Identity matrix |
| B. | $\begin{bmatrix} 1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$ | II. | Symmetric matrix |
| C. | $A-A^T$ | III. | Scalar matrix |
| D. | $\begin{bmatrix} 2 & 0 \\0 & 2\end{bmatrix}$ | IV. | Skew-symmetric matrix |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A-II, B-I, C-IV, D-III
(A) $(A+A^T)^T=A^T+(A^T)^T$
$=A^T+A$
$=A+A^T$
$⇒(A+A^T)$ is symmetric matrix.
(B) $\begin{bmatrix} 1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}$ → Identity Matrix
(C)
$(A-A^T)^T=A^T-(A^T)^T$
$=A^T-A$
$=-(A-A^T)$
$⇒(A-A^T)$ is skew-symmetric matrix.
(D) $\begin{bmatrix} 2 & 0 \\0 & 2\end{bmatrix}$ → Scalar Matrix