Match List – I with List – II.

Choose the correct answer from the options given below:

A-III, B-IV, C-I, D-II

The correct answer is Option (3) → A-III, B-IV, C-I, D-II

(A) $A^{-1}=\left[\begin{array}{ll}3 & 4 \\ 5 & 6\end{array}\right]$

$⇒A=(A^{-1})^{-1}=\left[\begin{array}{ll}-3 & 2 \\ \frac{5}{2} & -\frac{3}{2}\end{array}\right]$

(B) $A=\left[\begin{array}{cc}2 & -1 \\ 3 & 1\end{array}\right]$

$⇒A^T=\left[\begin{array}{cc}2 & 3 \\ -1 & 1\end{array}\right]$

$⇒AA^T=\left[\begin{array}{cc}2 & -1 \\ 3 & 1\end{array}\right]\left[\begin{array}{cc}2 & 3 \\ -1 & 1\end{array}\right]=\left[\begin{array}{cc}1 & 0 \\ 0 & 1\end{array}\right]$

Hence, there are called orthogonal matrix.

(C) $A^{-1}=\left[\begin{array}{ll}5 & 7 \\ 2 & 3\end{array}\right]$

$⇒(A^T)^{-1}=(A^{-1})^T=\left[\begin{array}{ll}5 & 2 \\ 7 & 3\end{array}\right]$

(D) $A=\left[a_{i j}\right]_{2 \times 2},a_{i j}=(i-j)^2$

$⇒A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$