1
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If A and B are two invertible square matrices of same order, then what is (AB)$$-$$1 equal to?
A
B$$-$$1 A$$-$$1
B
A$$-$$1 B$$-$$1
C
B$$-$$1 A
D
A$$-$$1 B
2
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following in respect of matrices A, B and C of same order.

1. (A + B + C)' = A' + B' + C'

2. (AB)' = A' B'

3. (ABC)' = C' B' A'

Where, A' is the transpose of the matrix A. Which of the above are correct?
A
1 and 2
B
2 and 3
C
1 and 3
D
1, 2 and 3
3
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Consider the following in respect of matrices A and B of same order.

1. A2 $$-$$ B2 = (A + B) (A $$-$$ B)

2. (A $$-$$ I) (I + A) = O $$ \Leftrightarrow $$ A2 = I

where, I is the identity matrix and O is the null matrix.

Which of the above is/are correct?
A
Only 1
B
Only 2
C
Both 1 and 2
D
Neither 1 nor 2
4
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
What is the adjoint of the matrix $$\left( {\matrix{ {\cos ( - \theta )} & { - \sin ( - \theta )} \cr { - \sin ( - \theta )} & {\cos ( - \theta )} \cr } } \right)$$ ?
A
$$\left( {\matrix{ {\cos \theta } & { - \sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right)$$
B
$$\left( {\matrix{ {\cos \theta } & {\sin \theta } \cr {\sin \theta } & {\cos \theta } \cr } } \right)$$
C
$$\left( {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right)$$
D
$$\left( {\matrix{ {\cos \theta } & { - \sin \theta } \cr {\sin \theta } & {\cos \theta } \cr } } \right)$$
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