If a_{ij}
= 1/2 (3*i* − 2*j* ) and A = [a_{ ij}]_{ 2×2} is

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option B**

**Explaination / Solution: **

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What must be the matrix X, if

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option A**

**Explaination / Solution: **

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Which one of the following is not true about the
matrix

**A. ** a scalar matrix

**B. ** a diagonal matrix

**C. ** an upper triangular matrix

**D. ** a lower triangular matrix

**Answer : ****Option B**

**Explaination / Solution: **

No Explaination.

No Explaination.

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If *A* and *B* are two matrices such that *A* + *B* and
*AB* are both defined, then

**A. ** A and B are two matrices not necessarily of same order

**B. ** A and B are square matrices of same order

**C. ** Number of columns of A is equal to the number of rows of B

**D. ** A = B.

**Answer : ****Option B**

**Explaination / Solution: **

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If A = then for what value of λ, A^{2}
= O ?

**A. ** 0

**B. ** ±1

**C. ** - 1

**D. ** 1

**Answer : ****Option B**

**Explaination / Solution: **

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If and ( A + B )^{2} = A^{2}
+ B^{2} then the values of *a*
and *b* are

**A. ** a = 4, b = 1

**B. ** a = 1, b = 4

**C. ** a = 0, b = 4

**D. ** a = 2, b = 4

**Answer : ****Option B**

**Explaination / Solution: **

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If is a matrix satisfying the
equation AA^{T} = 9I, where I is
3 × 3 identity matrix, then the ordered pair (*a, b*) is equal to

**A. ** (2, - 1)

**B. ** (- 2, 1)

**C. ** (2, 1)

**D. ** (- 2, - 1)

**Answer : ****Option D**

**Explaination / Solution: **

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If A is a square matrix, then which of the following is not symmetric?

**A. ** A + A^{T}

**B. ** AA^{T}

**C. ** A^{T}A

**D. ** A − A^{T}

**Answer : ****Option D**

**Explaination / Solution: **

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If A and B are symmetric matrices of order n, where ( A ≠ B), then

**A. ** A + B is skew-symmetric

**B. ** A + B is symmetric

**C. ** A + B is a diagonal matrix

**D. ** A + B is a zero matrix

**Answer : ****Option B**

**Explaination / Solution: **

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If A = and if *xy* = 1, then det ( AA^{T} ) is equal to

**A. ** (a −1)^{2}

**B. ** (a^{2} +1)^{2}

**C. ** a^{2} −1

**D. ** (a^{2} −1)^{2}

**Answer : ****Option D**

**Explaination / Solution: **

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