# Class 12 Mathematics Determinants: NCERT Solutions for Question 6

This page focuses on the detailed Determinants question answers for Class 12 Mathematics Determinants, addressing the question: 'If A = $$\begin{bmatrix}1 & 1 & -2\\2 & 1 & -3\\5 & 4 & -9\end{bmatrix}$$, Find |A|'. The solution provides a thorough breakdown of the question, highlighting key concepts and approaches to arrive at the correct answer. This easy-to-understand explanation will help students develop better problem-solving skills, reinforcing their understanding of the chapter and aiding in exam preparation.
Question 6

## If A = $$\begin{bmatrix}1 & 1 & -2\\2 & 1 & -3\\5 & 4 & -9\end{bmatrix}$$, Find |A|

Let  A = $$\begin{bmatrix}1 & 1 & -2\\2 & 1 & -3\\5 & 4 & -9\end{bmatrix}$$

By expanding along the first row, we have:

|A|  = 1$$\begin{vmatrix}1 & -3\\4 & -9\end{vmatrix}$$ - 1$$\begin{vmatrix}2 & -3\\5 & -9\end{vmatrix}$$  -  2$$\begin{vmatrix}2 & 1\\5 & 4\end{vmatrix}$$

= 1(-9 + 12) – 1(-18 + 15) -2(8 – 5)

= 1(3) – 1 (-3) – 2(3)

= 3 + 3 – 6

= 6 – 6

= 0