NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.4 Question 6

Question

Find the inverse, if it exists, of $\left[\begin{matrix}-1 & 5\-3 & 2\end{matrix}\right]$.

Accepted Answer

Final Answer: $\left[\begin{matrix}\frac{2}{13} & - \frac{5}{13}\\frac{3}{13} & - \frac{1}{13}\end{matrix}\right]$ Step 1: For a 2×2 matrix use det A=a₁₁a₂₂−a₁₂a₂₁. Step 2: $-2$ − $-15$ = $13$. Step 3: First check whether this determinant is zero. Step 4: The cofactor matrix is $\left[\begin{matrix}2 & 3\-5 & -1\end{matrix}\right]$. Step 5: Transpose the cofactor matrix: adj A=$\left[\begin{matrix}2 & -5\3 & -1\end{matrix}\right]$. Step 6: Divide by det A: A⁻¹=$\left[\begin{matrix}\frac{2}{13} & - \frac{5}{13}\\frac{3}{13} & - \frac{1}{13}\end{matrix}\right]$. Step 7: Multiplication verifies AA⁻¹=A⁻¹A=I.

NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.4 Question 6

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