Matrices in past papers.

CBSE Board Examination 2026

• Board 2026 Q2The order that cannot be a row matrix
  Types of matrices: row matrix1 mark
• Board 2026 Q3Which transpose properties are true
  Properties of the transpose1 mark
• Board 2026 Q6Which matrix is skew symmetric when $A$⁠, $B$ are
  Symmetric and skew symmetric matrices1 mark

CBSE Board Examination 2025

• Board 2025 Q1Inverse of $A = \text{diag}(-1, 1, 1)$
  Inverse of a diagonal matrix1 mark
• Board 2025 Q9Which of AB, AC, BA is defined?
  When a matrix product is defined1 mark
• Board 2025 Q13$y^x$ when a matrix is scalar
  Scalar matrix1 mark

CBSE Board Examination 2024

• Board 2024 Q2Possible orders of a matrix with 36 elements
  Order of a matrix1 mark
• Board 2024 Q5Find $\frac{24}{x} + \frac{24}{y}$ from equal matrices
  Equality of matrices1 mark
• Board 2024 Q18If $(A + B)^2 = A^2 + B^2$⁠, then $AB = -BA$
  Algebra of matrices: expanding (A + B)²1 mark

CBSE Board Examination 2023

• Board 2023 Q4B when $2A + B$ is a null matrix
  Addition and scalar multiples of matrices1 mark
• Board 2023 Q14x when $(3I + 4A)(3I - 4A) = x^2I$
  Multiplication of matrices1 mark

CBSE Sample Paper 2026-27

• Sample 2026-27 Q4Symmetric matrix: value of $\sqrt{6a + 2b + 3c}$
  Symmetric matrices1 mark
• Sample 2026-27 Q6Find $x$ when a product of three matrices is $O$
  Multiplication of matrices1 mark
• Sample 2026-27 Q26Find $PQ$ and $QP$ and the inverse of the product, if it exists
  Matrix products; inverse of a product matrix3 marks

CBSE Sample Paper 2025-26

• Sample 2025-26 Q2Orders $m, n, p, q$ when $AB$ and $AC$ are square
  Order of a product of matrices1 mark
• Sample 2025-26 Q3Value of $\frac{q + t}{p + r}$ for a skew-symmetric matrix
  Skew-symmetric matrices1 mark
• Sample 2025-26 Q32Find $AB$ and hence solve a system of three equations
  Inverse from AB = I; solving a system of equations5 marks

CBSE Sample Paper 2024-25

• Sample 2024-25 Q2Restrictions on $n, k, p$ so that $PY + WY$ is defined
  Order of matrices: when PY + WY is defined1 mark
• Sample 2024-25 Q7$a + b + c$ for a skew-symmetric matrix
  Skew-symmetric matrices1 mark

CBSE Sample Paper 2023-24

• Sample 2023-24 Q1$A^2$ when $a_{ij} = 1$ for $i \ne j$ and $0$ for $i = j$
  Constructing a matrix from a rule; A²1 mark

CBSE Sample Paper 2022-23

• Sample 2022-23 Q1Diagonal elements of a skew-symmetric matrix
  Skew-symmetric matrix: diagonal elements1 mark
• Sample 2022-23 Q10$(AB^{-1})^{-1}$ for non-singular $A$⁠, $B$
  Inverse of a product of matrices1 mark

CBSE Sample Paper 2020-21

• Sample 2020-21 Q4Order of $5A - 3B$ for $A_{3 \times n}$ and $B_{m \times 5}$
  Order of a matrix; addition of matrices1 mark
• Sample 2020-21 Q5$A^2$ for $a_{ij} = 1$ ($i \ne j$⁠), $0$ ($i = j$⁠). Or: $|\text{adj}\,A|$ when $|A| = -4$
  Constructing a matrix; |adj A| = |A|ⁿ⁻¹1 mark

Questions that also use Matrices

Their main topic is in another chapter.

• Board 2026 Q33Find $A^{-1}$ and solve a system, or the values of $x$ that make a matrix singular
  Inverse by adjoint, linear system; singular matrix5 marks
• Board 2025 Q15Which property of invertible matrices is not correct?
  Properties of the inverse and adjoint1 mark
• Board 2025 Q35Students in the Sports, Music and Drama clubs by the matrix method
  System of linear equations by the matrix method5 marks
• Board 2024 Q32Find $A^{-1}$ and solve a system of three equations, or find unknown entries from $A^{-1}$
  Inverse by adjoint; solving a linear system5 marks
• Board 2023 Q1$A^{-1} = xA + yI$ when $A^2 - 3A + I = O$
  Inverse of a matrix from a matrix equation1 mark
• Board 2023 Q33Find $(AB)^{-1}$ from $A$ and $B^{-1}$⁠, or solve a system by the matrix method
  Inverse of a product; system by matrix method5 marks
• Sample 2026-27 Q5$|\text{adj}(PQ)|$ for $2 \times 2$ matrices $P$ and $Q$
  Adjoint of a matrix: |adj A| = |A|ⁿ⁻¹1 mark
• Sample 2026-27 Q38Case study: fruit baskets, prices by the matrix inverse
  System of equations by the matrix inverse4 marks
• Sample 2025-26 Q5Inverse of the diagonal matrix $\operatorname{diag}(3, 2, 5)$
  Inverse of a diagonal matrix1 mark
• Sample 2024-25 Q33Path $y = ax^2 + bx + c$ of a headed football by the matrix method
  System of three equations by the matrix method5 marks
• Sample 2023-24 Q10$|A|$ for a $3 \times 3$ skew symmetric matrix in $x$
  Determinant of a skew symmetric matrix1 mark
• Sample 2023-24 Q34Matrix method: $\frac2x + \frac3y + \frac{10}{z} = 4$⁠, $\frac4x - \frac6y + \frac5z = 1$⁠, $\frac6x + \frac9y - \frac{20}{z} = 2$
  Matrix method: equations in 1/x, 1/y, 1/z5 marks
• Sample 2022-23 Q2$|AA'|$ when $|A'| = -3$
  Determinant of a product and of a transpose1 mark
• Sample 2022-23 Q35Find $A^{-1}$ and solve $2x - 3y + 5z = 11$⁠, $3x + 2y - 4z = -5$⁠, $x + y - 2z = -3$
  Inverse by the adjoint; solving a system by A⁻¹5 marks
• Sample 2020-21 Q20$|A|$ when $A^2 = 2A$⁠. Or: show $A^2 - 5A + 7I = O$ and find $A^{-1}$
  |kA| and |AB|; inverse from a matrix equation2 marks
• Sample 2020-21 Q36$A^{-1}$ and a system with matrix $A'$⁠, or $AB = 6I$ and a system
  Inverse of a matrix; solving a system of equations5 marks