Class XII Mathematics
Chapter 3: Matrices and Determinants
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Syllabus Sections
Key Formulas & Equations
Click Copy to duplicateMatrix Inverse Formula
A^{-1} = \frac{1}{|A|} \text{adj}(A)
Inverse of square matrix A using determinant and adjoint.
Determinant Expansion 2x2
\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc
Evaluation of 2x2 determinant.
Related Formulas from Adjacent Chapters
Sine Inverse range
\sin^{-1} x = \theta \Rightarrow \theta \in [-\frac{\pi}{2}, \frac{\pi}{2}]
[From Inverse Trigonometric Functions] Principal value branch for arcsin.
Power Rule of Differentiation
\frac{d}{dx}(x^n) = n x^{n-1}
[From Continuity and Differentiability] Differentiates exponential variable functions.
The Chain Rule
\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}
[From Continuity and Differentiability] Differentiates nested composite functions.