====== Question 2 and 3, Review Exercise ======
Solutions of Question 2 and 3 of Review Exercise of Unit 02: Matrices and Determinants. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. 

=====Question 2=====
For the matrix $A=\left[\begin{array}{ccc}1 & 2 & 0 \\ -3 & 4 & 9 \\ 2 & 1 & 6\end{array}\right]$; find $A_{13}, A_{23}$ and $A_{33}$; hence find $|A|$.

** Solution. **

Given: \begin{align*}
A&=\left[\begin{array}{ccc}1 & 2 & 0 \\ -3 & 4 & 9 \\ 2 & 1 & 6\end{array}\right]\\
A_{13} &= (-1)^{1+3} \left| \begin{array}{cc}
-3 & 4 \\
2 & 1
\end{array} \right| = -3 - 8 = -11\\
A_{23} &= (-1)^{2+3} \left| \begin{array}{cc}
1 & 2 \\
2 & 1
\end{array} \right| = -(1 - 4) = 3\\
A_{33} &= (-1)^{3+3} \left| \begin{array}{cc}
1 & 2 \\
-3 & 4
\end{array} \right| = 4 +6 = 10\\
|A|&= 1(24-9)-2(-18-18)+0\\
&=15+72\\
&=87
\end{align*}




=====Question 3=====
Prove that if $A^{-1}=A^{t}$ then $\left|A A^{t}\right|=1$.FIXME

** Solution. **



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