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Matrices - ISC Class 12 Mathematics Questions with Answers

50 past-paper questions on Matrices from ISC Class 12 Mathematics papers (2027-2017), newest first. Open one to see its answer.

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A ball is thrown vertically downwards from the top of a cliff, and its position is tracked from when it is first thrown until it… 2027 · 5 marks · Short answer
Using the properties of matrices, explain why the following concept is incorrect: Since $(a+b)(a-b) = a^2 - b^2$, therefore… 2027 · 1 mark · Short answer
A school is organising its Annual Day function and plans to decorate every chair with a ribbon and every table with a cover… 2027 · 3 marks · Short answer
Vinayak runs a bakery shop. He sells three items: Sandwiches (₹$x$ per unit), Fruit juices (₹$y$ per unit) and Cookies (₹$z$ per… 2026 · 4 marks · Short answer
To raise money for an orphanage, students of three schools A, B and C organised an exhibition in their residential colony, where… 2026 · 6 marks · Short answer
In subparts (i) to (xi) choose the correct options and in subparts (xii) to (xv), answer the questions as instructed. If A and B… 2026 · 15 marks · Short answer
If $A = \begin{bmatrix} 1 & -2 & 0 \\ 2 & -1 & -1 \\ 0 & -2 & 1 \end{bmatrix}$, then find $A^{-1}$. Using $A^{-1}$, solve the… 2026 · 4 marks · Short answer
If $A$ and $B$ are matrices of same order, then $AB' - BA'$ is a: 2026 · 1 mark · MCQ
How many possible matrices can be formed of order $3 \times 3$ if each entry is either $0$ or $1$? 2026 · 1 mark · MCQ
If $\begin{bmatrix} 2x & 3 \end{bmatrix} \begin{bmatrix} 1 & 2 \\ -3 & 0 \end{bmatrix} \begin{bmatrix} x \\ 3 \end{bmatrix} = O$… 2026 · 1 mark · MCQ
The system of three linear equations in three unknown variables can be written in the matrix form as $AX = B$. It has a unique… 2026 · 1 mark · Assertion-reason
Three shopkeepers Gaurav, Rizwan and Jacob use carry bags made of polythene, handmade paper and newspaper. The number of… 2025 · 2 marks · Short answer
In a market survey, three commodities A, B and C were studied. Each commodity had three varieties. To find out the index number… 2025 · 2 marks · Short answer
If $A = \begin{bmatrix} 0 & 5 & -y \\ -5 & 0 & x \\ y & -x & 0 \end{bmatrix}$, then the value of… 2025 · 1 mark · MCQ
If a matrix $A = [a_{ij}]_{2 \times 2}$, where $a_{ij} = \begin{cases} 1, & i \neq j \\ 0, & i = j \end{cases}$, then $A^{-1}$ is: 2025 · 1 mark · MCQ
Statement 1: Every scalar matrix is a diagonal matrix. Statement 2: Every diagonal matrix is an identity matrix. 2025 · 1 mark · MCQ
The matrix $A = \begin{bmatrix} a & 6 & b \\ 2c & x+1 & 8 \\ -1 & -8 & y-3 \end{bmatrix}$ is a skew symmetric matrix, then find… 2025 · 1 mark · Short answer
Let $A = \begin{bmatrix} d_1 & 0 & 0 \\ 0 & d_2 & 0 \\ 0 & 0 & d_3 \end{bmatrix}$, then… 2025 · 1 mark · Assertion-reason
In the third-order matrix, $a_{ij}$ denotes the element of the $i^{\text{th}}$ row and $j^{\text{th}}$ column… 2025 · 1 mark · MCQ
Statement 1: If '$A$' is an invertible matrix, then $(A^2)^{-1} = (A^{-1})^2$ Statement 2: If '$A$' is an invertible matrix, then… 2025 · 1 mark · MCQ
For what value of $x$, is $A = \begin{bmatrix} 0 & 1 & -2 \\ -1 & 0 & 3 \\ x & -3 & 0 \end{bmatrix}$ a skew symmetric matrix? 2025 · 1 mark · One word
In subparts (i) to (xi) choose the correct options and in subparts (xii) to (xv), answer the questions as instructed. A matrix… 2025 · 15 marks · Short answer
If $A = \begin{bmatrix} 0 & a \\ 0 & 0 \end{bmatrix}$, then $A^{16}$ is: 2025 · 1 mark · MCQ
A furniture factory uses three types of wood namely, teakwood, rosewood and satinwood for manufacturing three types of furniture… 2024 · 6 marks · Short answer
If $A$ and $B$ are symmetric matrices of the same order, then $AB - BA$ is: 2024 · 1 mark · MCQ
Let the matrices $A = \begin{bmatrix} -3 & 2 \\ -5 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} 4 & -2 \\ 5 & -3 \end{bmatrix}$ be… 2024 · 1 mark · Assertion-reason
Use matrix method to solve the following system of equations: $\frac{2}{x} + \frac{3}{y} + \frac{10}{z} = 4$… 2023 · 6 marks · Short answer
If $A = \begin{pmatrix} 1 & b \\\\ 0 & 1 \end{pmatrix}$, then $A^n$ ($n \in \mathbb{N}$) is equal to 2023 · 1 mark · MCQ
For what value of $k$ the matrix $\begin{bmatrix} 0 & k \\ -6 & 0 \end{bmatrix}$ is a skew symmetric matrix? 2023 · 1 mark · One word
Find $A^{-1}$, if $A = \begin{pmatrix} 1 & 2 & 0 \\\\ -2 & -1 & -2 \\\\ 0 & -1 & 1 \end{pmatrix}$. Using $A^{-1}$, solve the… 2023 · 6 marks · Long answer
If $\begin{pmatrix} 3 & 5 \\\\ 7 & 9 \end{pmatrix} = X + Y$, where $X$ is skew-symmetric matrix and $Y$ is symmetric matrix. Find… 2023 · 1 mark · Short answer
What is the multiplicative inverse of matrix $A$? 2022 · 2 marks · MCQ
From the matrix equation $AB = AC$, it can be concluded that $B = C$ provided: 2022 · 2 marks · MCQ
If $A$ and $B$ are two non singular matrices, and $AB$ exists, then $(AB)^{-1}$ is: 2022 · 2 marks · MCQ
What is the transpose of a column matrix? 2022 · 2 marks · MCQ
Solve the matrix equation… 2021 · 6 marks · Short answer
If $A = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$, then $A^2$ is equal to: 2021 · 1 mark · MCQ
Using matrices, solve the following system of equations: $2x - 3y + 5z = 11$, $3x + 2y - 4z = -5$ and $x + y - 2z = -3$ 2021 · 6 marks · Short answer
Solve the following system of linear equations using matrices: $x - 2y = 10, \quad 2x - y - z = 8, \quad -2y + z = 7$ 2020 · 6 marks · Short answer
If… 2020 · 2 marks · Numerical
Solve the following system of linear equations using matrix method: $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 9$… 2019 · 6 marks · Long answer
Show that $(A + A')$ is symmetric matrix, if $A = \begin{pmatrix} 2 & 4 \\\\ 3 & 5 \end{pmatrix}$. 2019 · 2 marks · Derivation
If $A = \begin{pmatrix} 5 & a \\ b & 0 \end{pmatrix}$ and $A$ is a symmetric matrix, show that $a = b$. 2018 · 2 marks · Derivation
Evaluate… 2018 · 6 marks · Long answer
Using elementary transformations, find the inverse of the matrix… 2018 · 6 marks · Long answer
Using matrices, solve the following system of equations: $2x - 3y + 5z = 11$ $3x + 2y - 4z = -5$ $x + y - 2z = -3$ 2018 · 6 marks · Short answer
Using elementary transformation, find the inverse of the matrix… 2018 · 6 marks · Short answer
Find the value of $k$ if $M = \begin{pmatrix} 1 & 2 \\ 2 & 3 \end{pmatrix}$ and $M^2 - kM - I_2 = 0$. 2018 · 2 marks · Short answer
Given that: $A = \begin{pmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{pmatrix}$ and… 2017 · 5 marks · Short answer
If the matrix $\begin{pmatrix} 6 & -x^2 \\ 2x - 15 & 10 \end{pmatrix}$ is symmetric, find the value of $x$. 2017 · 3 marks · Numerical

Matrices - ISC Class 12 Mathematics Questions with Answers

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