1
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $A$ and $B$ are both $3 \times 3$ matrices, then which of the following statements are true?

(i) $A B=0 \Rightarrow A=0$ or $B=0$

(ii) $A B=I_3 \Rightarrow A^{-1}=B$

(iii) $(A-B)^2=A^2-2 A B+B^2$

A

(i) is false and (ii), (iii) are true

B

(ii) is true (i), (iii) are false

C

(i) and (ii) are true, (iii) is false

D

All are true

2
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$A=\left[\begin{array}{ccc}1 & -1 & 2 \\ -2 & 3 & -3\end{array}\right]$ is the given matrix and $A^T$ represents the transpose of $A$, then $A A^T-A-A^T=$

A

$\left[\begin{array}{ccc}4 & 8 & 12 \\ 8 & 16 & -28 \\ 12 & -28 & 47\end{array}\right]$

B

$\left[\begin{array}{ccc}4 & -8 & 12 \\ -8 & 16 & -28 \\ 12 & -28 & 47\end{array}\right]$

C

$\left[\begin{array}{ccc}4 & -8 & 12 \\ -8 & 16 & 28 \\ 12 & 28 & 47\end{array}\right]$

D

$\left[\begin{array}{ccc}4 & -8 & -12 \\ -8 & 16 & -28 \\ -12 & -28 & 47\end{array}\right]$

3
AP EAPCET 2025 - 21st May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $A=\left[\begin{array}{ccc}x & 2 & 1 \\ -2 & y & 0 \\ 2 & 0 & -1\end{array}\right], x$ and $y$ are non-zero numbers, trace of $A=0$ and determinant of $A=-6$, then the minor of the elements 1 of $A$ is

A

-4

B

4

C

2

D

-2

4
AP EAPCET 2024 - 23th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
4. If $A=\left[\begin{array}{lll}83 & 74 & 41 \\ 93 & 96 & 31 \\ 24 & 15 & 79\end{array}\right]$, then $\operatorname{det}\left(A-A^T\right)$ is equal to
A
0
B
-7851
C
2442
D
1

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