NCERT Mathematics, Class 12, textbook pages 34–75 (Part I)

How to help your child with Class 12 Maths Chapter 3, Matrices, at home

Types, operations and transpose, explained for parents: a 60-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

[1 2] [5 6] [19 22][3 4] [7 8] = [43 50]AB ≠ BA in general

NCERT Class 12 Maths Chapter 3 Matrices: what it teaches

Your teen organises data in matrices, adds and multiplies them, understands order and when multiplication is possible, finds transposes, and works with symmetric and skew-symmetric matrices.

Why it matters later. Matrices are used in determinants, solving systems, computer graphics and data science.

See it: this chapter in pictures

(2 × 3)(3 × 4)inner 3 = 3 ✓result 2 × 4
Inner dimensions must match.
A = ½(A + Aᵀ) + ½(A − Aᵀ)symmetric + skew-symmetricevery square matrix
Any square matrix splits this way.
quantities × prices= billsmatrices organise data
Real data in matrix form.

You need

  • price and quantity tables
  • a calculator

Tonight’s 60 minutes

  1. Put prices of 3 items at 2 shops in a matrix.
  2. Multiply a quantity matrix by a price matrix to get bills.
  3. Show AB ≠ BA with 2 × 2 examples.
  4. Write a matrix as a sum of symmetric and skew-symmetric parts.

Words to use

  • matrix
  • order
  • transpose
  • symmetric
  • skew-symmetric
  • identity matrix

Watch for

  • Multiplying incompatible orders. Columns of A must equal rows of B.
  • Assuming AB = BA. Matrix multiplication isn’t commutative; test it.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

You2 × 3 times 3 × 4?

Your childInner 3s match: 2 × 4 result.

A game for this week: Shop bill matrix

  1. Make quantity and price matrices for two families.
  2. Multiply to find bills.
  3. Check by direct adding.
  4. Swap data.

A 5-day plan, 60 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Spreadsheets.
  • Computer graphics transforms.
  • Economics tables.
  • Machine learning.

Quick check

Ask these at the end of the week. Tap to see the answer.

Order of product of 2 × 3 and 3 × 4 matrices?

2 × 4.

(Aᵀ)ᵀ = ?

A.

Is AB = BA always?

No.

Ready for the next chapter when your child…

  • Performs matrix operations.
  • Finds transposes.
  • Identifies symmetric and skew-symmetric matrices.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 12). See the full Class 12 parent guide for every chapter.

Questions parents ask

When can two matrices be multiplied?

When the first’s columns equal the second’s rows.

What is a symmetric matrix?

A matrix equal to its transpose.

Why learn matrices?

They organise and transform data in science and computing.