PYQ Vault
EbooksTutor

Property

Matrix multiplication is not commutative

(A+B)(A−B)=A2−AB+BA−B2(A+B)(A-B) = A^2 - AB + BA - B^2
AB,BAAB, BA
the two orders of the product

Because AB and BA generally differ, the familiar algebraic identities hold only when the two matrices commute, and the cross terms must be kept separate until then.

15
questions use it
9
of them past-year
2018–2026
years it has appeared
13%
rated HARD
2
exams
Matrices & Determinants notesOpen all 15 in the paper builder

Used alongside

How often each of these appears in the same solution as this one.

15 questions whose solution uses this

Every one was read individually — a question is here because its solution invokes this, not because the stem mentions it.

Filter

Filter by exam
Filter by past-year or practice

Showing 15 of 15 questions — easiest first, then oldest paper first.

  • #1NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #2NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #3CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #4NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #5NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #6NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #7NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #8CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #9CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #10CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #11CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #12CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

    Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.

  • #13CBSE Class 12 → Mathematics → Matrices → Multiplication of Matrices

  • #14NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

  • #15NDA → Mathematics → Matrices & Determinants → Matrix Operations, Polynomials, and Equations

Every identity this chapter tests, with its own question set.

All Matrices & Determinants formulas