Matrices — Class 12 CBSE Mathematics revision notes
A 3-page visual revision sheet for Matrices, written for Class 12 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Matrices in one look
a rectangular array with its own arithmetic: familiar rules, one big exception
A matrix, defined
- order (rows × columns)
m × n - general entry, row i column j
A = [a_ij] - total entries in an m×n matrix
mn
Types, by shape
- Row matrix: order 1×n, a single row
- Column matrix: order m×1, a single column
- Square matrix: order n×n, rows = columns
- Zero matrix: every entry 0, any order, written O
Types, by what's inside a square matrix
- Diagonal matrix: square, every off-diagonal entry is 0
- Scalar matrix: diagonal, and every diagonal entry is the same number
- Identity matrix I: scalar, with every diagonal entry = 1
Addition, subtraction, scalar multiplication
- addition, same order required
(A+B)_ij = a_ij+b_ij - subtraction
A-B = A+(-1)B - scalar multiple
(kA)_ij = k a_ij
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Matrices sheet covers
- A matrix, defined
- order (rows × columns)
- general entry, row i column j
- total entries in an m×n matrix
- Types, by shape
- Row matrix
- Column matrix
- Square matrix
- Zero matrix
- Types, by what's inside a square matrix
- Diagonal matrix
- Scalar matrix
- Identity matrix I
- Addition, subtraction, scalar multiplication
- addition, same order required
- subtraction
- scalar multiple
- Matrix multiplication
- defined only when
- result order
- entry (i,j) of the product
- Multiplying by the special ones
- By the identity
- By the zero matrix
- Multiplication is NOT commutative
- in general
- order can flip whether it's even defined
- Transpose
- Elementary row and column operations
- Invertible matrices
- A is invertible when some B satisfies
- that B is called
- only these can qualify at all
- Finding A⁻¹ by row operations
- Inverse of a product reverses order
- if A and B are both invertible
- Symmetric vs Skew-symmetric
- Symmetric
- Skew-symmetric
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Matrices the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.