Matrices: 2 marks Questions (CBSE Class 12)

4 different 2 marks questions on Matrices from CBSE Class 12 Maths board exams 2024–2026, newest first.

Q212 marksVery Short AnswerMatrices CBSE 2025 · 65/4/3

If $A = [2 - 2 - 2 2]$ and $A^{2} = k A$ , then find the value of k.

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Answer: k = 4

Q222 marksVery Short AnswerMatrices CBSE 2025 · 65/7/1

If $A = [2 - 1 32]$ , then show that $A^{2} - 4 A + 7 I = 0$ .

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Answer: Proved.

$A^{2} = [4 - 3 - 2 - 2 6 + 6 - 3 + 4] = [1 - 4 121]$ .
$4 A = [8 - 4 128]$ , $7 I = [7007]$ .
$A^{2} - 4 A + 7 I = [1 - 8 + 7 - 4 + 4 + 0 12 - 12 + 0 1 - 8 + 7] = [0000] = 0$ .

Q222 marksVery Short AnswerMatrices CBSE 2025 · 65/7/2

If $302 - 1 1 - 3 A = 2 - 5 - 17$ , then find matrix A.

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Answer:

A = [- 1 - 5]

from the first two rows (the third row is not satisfied as printed)

A must be of order $2 \times 1$ ; let $A = [x y]$ .
Multiplying: $3 x - y = 2$ , $y = - 5$ , $2 x - 3 y = - 17$ .
From the first two equations: $y = - 5$ and $3 x = - 3$ , so $x = - 1$ .
But then $2 x - 3 y = - 2 + 15 = 13 \neq = - 17$ , so the printed system has no exact solution.
The intended answer is $A = [- 1 - 5]$ (it fits if the last entry is 13).

Q222 marksVery Short AnswerMatrices CBSE 2025 · 65/7/3

If $A = [1 - 1 05]$ , then find the value of K if $A^{2} = 6 A + K I_{2}$ , where $I_{2}$ is an identity matrix.

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Answer: K = −5

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