Matrices — Class 12 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Matrices" — 8 important questions with detailed answers for CBSE board exam preparation.

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TL;DR: Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Matrices" — 8 important questions with detailed answers for CBSE board exam prepar…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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Key Questions Covered:

Find x and y if [x+y, 2y] = [7, 8].
If A = [1 2; 3 4] and B = [2 0; 1 3], find A + B.
If A = [1 2 3; 4 5 6] and k = 2, find kA.
If A = [1 2; 3 4], find A² (i.e., A × A).
If A = [2 3; 1 4], find the transpose of A (denoted Aᵀ).
Compute A - 2B if A = [5 3; 2 1] and B = [1 2; 0 3].
+ 2 more questions in the full chapter

Solutions Summary:

Question	Status
Find x and y if [x+y, 2y] = [7, 8].	✓ Solved
If A = [1 2; 3 4] and B = [2 0; 1 3], find A + B.	✓ Solved
If A = [1 2 3; 4 5 6] and k = 2, find kA.	✓ Solved
If A = [1 2; 3 4], find A² (i.e., A × A).	✓ Solved
If A = [2 3; 1 4], find the transpose of A (denoted Aᵀ).	✓ Solved
Compute A - 2B if A = [5 3; 2 1] and B = [1 2; 0 3].	✓ Solved

Showing 6 of 8 questions

Q1: Find x and y if [x+y, 2y] = [7, 8].

Given: [x + y, 2y] = [7, 8] Two matrices (or arrays) are equal if and only if their corresponding elements are equal. Comparing corresponding elements: First element: x + y = 7 ... (1) Second element: 2y = 8 ... (2) From equation (2): 2y = 8 y = 4 Substituting y = 4 into equation (1): x + 4 = 7 x = 3 VERIFICATION: [x + y, 2y] = [3 + 4, 2(4)] = [7, 8] ✓ CONCLUSION: x = 3 and y = 4

Q2: If A = [1 2; 3 4] and B = [2 0; 1 3], find A + B.

Given: A = [1 2; 3 4] and B = [2 0; 1 3] To find A + B, add corresponding elements: A + B = [1 2; 3 4] + [2 0; 1 3] = [1+2, 2+0; 3+1, 4+3] = [3, 2; 4, 7] CONCLUSION: A + B = [3 2; 4 7]

Q3: If A = [1 2 3; 4 5 6] and k = 2, find kA.

Given: A = [1 2 3; 4 5 6] and k = 2 Scalar multiplication of a matrix is performed by multiplying each element by the scalar: kA = 2 × [1 2 3; 4 5 6] = [2×1, 2×2, 2×3; 2×4, 2×5, 2×6] = [2, 4, 6; 8, 10, 12] CONCLUSION: kA = [2 4 6; 8 10 12]

Q4: If A = [1 2; 3 4], find A² (i.e., A × A).

Given: A = [1 2; 3 4] We need to find A × A. For multiplication, the element at position (i,j) in the result is the dot product of row i of the first matrix and column j of the second matrix. A² = [1 2; 3 4] × [1 2; 3 4] Element (1,1): (1)(1) + (2)(3) = 1 + 6 = 7 Element (1,2): (1)(2) + (2)(4) = 2 + 8 = 10 Element (2,1): (3)(1) + (4)(3) = 3 + 12 = 15 Element (2,2): (3)(2) + (4)(4) = 6 + 16 = 22 A² = [7, 10; 15, 22] CONCLUSION: A² = [7 10; 15 22]

Q5: If A = [2 3; 1 4], find the transpose of A (denoted Aᵀ).

Given: A = [2 3; 1 4] The transpose of a matrix A is obtained by interchanging its rows and columns. Rows of A: Row 1 = [2, 3], Row 2 = [1, 4] Columns of A: Column 1 = [2; 1], Column 2 = [3; 4] Aᵀ (transpose) has columns of A as its rows: Aᵀ = [2, 1; 3, 4] Alternatively, element at position (i, j) in Aᵀ equals element at position (j, i) in A. VERIFICATION: A₁₁ = 2 → (Aᵀ)₁₁ = 2 ✓ A₁₂ = 3 → (Aᵀ)₂₁ = 3 ✓ A₂₁ = 1 → (Aᵀ)₁₂ = 1 ✓ A₂₂ = 4 → (Aᵀ)₂₂ = 4 ✓ CONCLUSION: Aᵀ = [2 1; 3 4]

Q6: Compute A - 2B if A = [5 3; 2 1] and B = [1 2; 0 3].

Given: A = [5 3; 2 1] and B = [1 2; 0 3] Step 1: Find 2B 2B = 2 × [1 2; 0 3] = [2, 4; 0, 6] Step 2: Find A - 2B A - 2B = [5 3; 2 1] - [2 4; 0 6] = [5-2, 3-4; 2-0, 1-6] = [3, -1; 2, -5] CONCLUSION: A - 2B = [3 -1; 2 -5]

Showing 6 of 8 questions. Visit the full page for complete solutions.

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