Exam Questions & Step-by-Step Markschemes (220 Problems)
Question 1 • 2023
1 Marks
If for a square matrix A, A^2 - 3A + I = O and A^{-1} = xA + yI , then the value of x + y is :
Answer: (B) 2
Question 2 • 2023
1 Marks
If |A| = 2 , where A is a 2 \times 2 matrix, then |4A^{-1}| equals :
Answer: (C) 8
Question 3 • 2023
1 Marks
Let A be a 3 \times 3 matrix such that |\text{adj } A| = 64 . Then |A| is equal to :
Answer: (D) 8 or -8
Question 4 • 2023
1 Marks
If A = \begin{bmatrix} 3 & 4 \\ 5 & 2 \end{bmatrix} and 2A + B is a null matrix, then B is equal to :
Answer: (B) \begin{bmatrix} -6 & -8 \\ -10 & -4 \end{bmatrix}
Question 5 • 2023
1 Marks
If A = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} and (3I + 4A)(3I - 4A) = x^2I , then the value(s) x is/are :
Answer: (C) \pm 5
Question 6 • 2023
5 Marks
If A = \begin{bmatrix} 1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1 \end{bmatrix} and B^{-1} = \begin{bmatrix} 3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2 \end{bmatrix} , find (AB)^{-1} .
Answer: (AB)^{-1} = \begin{bmatrix} 10 & 7 & 21 \\ -49 & -34 & -103 \\ 17 & 12 & 36 \end{bmatrix}