If | adj(adj *A*) |=| *A *|^{9 }, then the order of the square matrix *A *is

**A. ** 3

**B. ** 4

**C. ** 2

**D. ** 5

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

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If *A *is a 3× 3 non-singular matrix such that *AA*^{T }= *A*^{T }A and *B *= *A*^{−1 }*A*^{T }, then *BB*^{T }=

**A. ** A

**B. ** B

**C. ** I_{3}

**D. ** B^{T}

**Answer : ****Option C**

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If A = , B = adj A and C = 3*A *, then =

**A. ** 1/3

**B. ** 1/9

**C. ** 1/4

**D. ** 1

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

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if , then A =

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option C**

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if , then *9I*_{2} – A =

**A. ** *A*^{-1}

**B. ** *A*^{-1}/2

**C. ** 3*A*^{-1}

**D. ** 2*A*^{-1}

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

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if A = , B= then | adj ( *AB*) |=

**A. ** -40

**B. ** -80

**C. ** -60

**D. ** -20

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

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If P= is the adjoint of 3× 3 matrix *A *and | *A *|= 4 , then *x *is

**A. ** 15

**B. ** 12

**C. ** 14

**D. ** 11

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

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If *A*= , and *A*^{−1 }= then the value of *a*_{23
}is

**A. ** 0

**B. ** -2

**C. ** -3

**D. ** -1

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

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If *A*, *B *and *C
*are invertible matrices of some order, then which one of the following is
not true?

**A. ** adj A =| A | A^{-1}

**B. ** adj(
AB) = (adj A)(adj B)

**C. ** det A^{-1} = (det
A)^{-1}

**D. ** ( ABC)^{-1} = C^{-1}B^{-1}A^{-1}

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

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If ( *AB*)^{−1 }= , and A^{-1} = , then *B*^{−1 }=

**A. **

**B. **

**C. **

**D. **

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

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