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CBSE · Class 12 · Mathematics

Matrices

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
The number of possible orders of a matrix with 18 elements is:
  1. 7
  2. 5
  3. 12
  4. 6
2.
A = [aij] is a 2 × 2 matrix with aij = 4i − 4j. Then A is:
  1. −16−32−32−64
  2. 04−40
  3. 1−351
  4. 0−440
3.
If A = −42−55 and B = 250−2, then −3A + B is:
  1. −1011−1513
  2. 14−115−17
  3. −10−13−511
  4. 10−1115−13
4.
If A = 2−211 and B = 4−11−3, then AB is:
  1. 645−4
  2. 6−32−2
  3. 7−9−1−5
  4. 821−3
5.
A matrix with m rows and n columns has order:
  1. m + n
  2. n × m
  3. m × n
  4. mn × 1
6.
If A = 9−37962, then Aᵀ is:
  1. 99−3672
  2. 72−3699
  3. 996−327
  4. 276−399
7.
If x + y−99x − y = 14−990, then:
  1. x = 7, y = −7
  2. x = −7, y = −7
  3. x = 7, y = 7
  4. x = 14, y = 0
8.
Assertion (A): The matrix 63536454−3 is symmetric.
Reason (R): A square matrix A is symmetric when Aᵀ = A.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
If A = 562526 and B = 3−1315−1, find A + B and A − B.
10.
Find AB if A = 433011 and B = −3−3−1442.
11.
If A = −1033, find A2 and show that A2 − 2A − 3I = O.
12.
Construct the 2 × 3 matrix A = [aij] with aij = i2 + 4j.
13.
Express A = 5−5−1027−426 as the sum of a symmetric matrix P and a skew-symmetric matrix Q.
14.
Find x, y, z and w if 3xyzw + −3162 = 152215−1.
15.
Find the matrix X such that 3X + A = B, where A = 0−4−26 and B = −1211−512.
16.
If A = −14−3−2 and B = −34−20, find AB and BA. Is AB = BA?
Section C — Word problems4 × 4 = 16 marks
17.
Shop R sold 52 notebooks, 58 pens, 50 files; Shop Q sold 32 notebooks, 19 pens, 10 files. The prices are Rs 12 per notebook, Rs 23 per pen, Rs 20 per file. Use matrix multiplication to find each shop's sales.
18.
For A = 53−24−135−25, find Aᵀ, A + Aᵀ and A − Aᵀ. Show that A + Aᵀ is symmetric and A − Aᵀ is skew-symmetric, and write A as their combination.
19.
If f(x) = x2 + 2x − 5 and A = 1−23−1, find f(A).
20.
A trust has Rs 52,000 to invest in two bonds paying 8% and 10% interest a year. Using matrix multiplication, find how the money should be split to earn Rs 4,920 a year.
AmbifulWorksheets
Practice that never repeats
CBSE · Class 12 · Mathematics

Answer key

Matrices · AW-12M-MAT-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 6the orders are m × n with mn = 18: one for each divisor of 18
2(d) 0−440a12 = 4(1) − 4(2) = −4
3(b) 14−115−17multiply each entry of A by −3, then add B
4(a) 645−4row of A times column of B
5(c) m × n—
6(a) 99−3672rows become columns
7(c) x = 7, y = 7x + y = 14 and x − y = 0
8(a) Both A and R are true, and R is the correct explanation of A.A is true: aij = aji for every i and j. R is true and explains A.
9A + B = 855675; A − B = 27−14−37add or subtract matching entries
10−3636a11 = 4(−3) + 3(−1) + 3(4)
11A2 = 1069; A2 − 2A − 3I = 00002A = −2066, −3I = −300−3
12591381216a23 = 16
13P = 5−5/2−5/2−5/229/2−5/29/26, Q = 0−5/23/25/205/2−3/2−5/20P = (A + Aᵀ)/2, Q = (A − Aᵀ)/2
14x = 6, y = 7, z = 3, w = −13x − 3 = 15
15X = −45−12X = (B − A)/3
16AB = −5−413−12; BA = −9−202−8; AB ≠ BAmultiply both ways
17Shop R: Rs 2,958; Shop Q: Rs 1,021525850321910 × 122320 = 29581021
18Aᵀ = 5453−1−2−235; A + Aᵀ = 10737−213110; A − Aᵀ = 0−1−71057−50; A = 57/23/27/2−11/23/21/25 + 0−1/2−7/21/205/27/2−5/20A = ½(A + Aᵀ) + ½(A − Aᵀ)
19f(A) = −8−46−12A2 = −500−5; f(A) = A2 + 2A − 5I
20Rs 14,000 at 8% and Rs 38,000 at 10%[x, 52000 − x] × 8/10010/100 = 4920