CBSE 12 Math · U2
Algebra
Matrices and determinants, including matrix operations, inverse matrices, adjoints, area using determinants, and systems of linear equations.
Test yourself
A focused, distraction-free run through 35 multiple-choice questions. Hints if you need them; your score at the end.
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Topic 2.1
Matrix Notation, Order, Equality, and Types
CBSE-style basics of matrix entries, order, equality, diagonal and special matrices.
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Topic 2.2
Operations on Matrices
Addition, subtraction, scalar multiplication, matrix multiplication, and non-commutativity.
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Topic 2.3
Transpose, Symmetric, and Skew-Symmetric Matrices
Transpose operations, symmetric and skew-symmetric conditions, and decomposition.
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Topic 2.4
Invertible Matrices and Matrix Equations
Invertibility of square matrices, inverse of $2\times2$ matrices, uniqueness, and matrix equations.
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Topic 2.5
Determinants, Minors, and Cofactors
Evaluating determinants up to order $3$, and computing minors and cofactors.
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Topic 2.6
Adjoint, Inverse, and Area Using Determinants
Adjoint and inverse of matrices, plus determinant formula for area of a triangle.
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Topic 2.7
Systems of Linear Equations Using Matrices
Consistency, uniqueness, and solving systems of linear equations using inverse matrices.
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