If A = [a_ij] is a square matrix of order 2 such that a_ij = cases 2, & when i ≠ j \\ 0, & when i = j cases, then det (A^2) is: Option 1: 0 Option 2: 2 Option 3: 8 Option 4: 16

Answer: 16. Solution: For a 2×2 matrix A where each element a_ij follows the given rule: - When i ≠ j (off-diagonal): a_ij = 2 - When i = j (diagonal): a_ij = 0 A = bmatrix a_11 & a_12 \\ a_21 & a_22 bmatrix For each element: a_11: Here i = 1, j = 1 → i = j → a_11 = 0 a_12: Here i = 1, j = 2 → i ≠ j → a_12 = 2 a_21: Here i = 2, j = 1 → i ≠ j → a_21 = 2 a_22: Here i = 2, j = 2 → i = j → a_22 = 0 Therefore: A = bmatrix 0 & 2 \\ 2 & 0 bmatrix For a 2×2 matrix bmatrix a & b \\ c & d bmatrix, determinant = ad - bc (A) = (0)(0) - (2)(2) (A) = 0 - 4 (A) = -4 Using the property (A^2) = [(A)]^2: (A^2) = (-4)^2 (A^2) = 16

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If $A = [a_{ij}]$ is a square matrix of order 2 such that $a_{ij} = \begin{cases} 2, & \text{when } i \neq j \\ 0, & \text{when } i = j \end{cases}$ , then det $(A^2)$ is:

✅ Correct Option: 4

For a 2×2 matrix A where each element $a_{ij}$ follows the given rule:

When $i \neq j$ (off-diagonal): $a_{ij} = 2$
When $i = j$ (diagonal): $a_{ij} = 0$

$A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$

For each element:

$a_{11}$ : Here $i = 1, j = 1$ → $i = j$ → $a_{11} = 0$

$a_{12}$ : Here $i = 1, j = 2$ → $i \neq j$ → $a_{12} = 2$

$a_{21}$ : Here $i = 2, j = 1$ → $i \neq j$ → $a_{21} = 2$

$a_{22}$ : Here $i = 2, j = 2$ → $i = j$ → $a_{22} = 0$

Therefore:

$A = \begin{bmatrix} 0 & 2 \\ 2 & 0 \end{bmatrix}$

For a 2×2 matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ , determinant $= ad - bc$

$\det(A) = (0)(0) - (2)(2)$

$\det(A) = 0 - 4$

$\det(A) = -4$

Using the property $\det(A^2) = [\det(A)]^2$ :

$\det(A^2) = (-4)^2$

$\det(A^2) = 16$

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Choose the correct answer from the options given below:

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If A=[aij]A = [a_{ij}]A=[aij​] is a square matrix of order 2 such that aij={2,when i≠j0,when i=ja_{ij} = \begin{cases} 2, & \text{when } i \neq j \\ 0, & \text{when } i = j \end{cases}aij​={2,0,​when i=jwhen i=j​, then det (A2)(A^2)(A2) is:

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CUET Mathematics Past Year Questions (Topic-Wise)

If $A = [a_{ij}]$ is a square matrix of order 2 such that $a_{ij} = \begin{cases} 2, & \text{when } i \neq j \\ 0, & \text{when } i = j \end{cases}$ , then det $(A^2)$ is: