If A = bmatrix a & b \\ c & (1+bc)/a bmatrix, then aA^(-1) is equal to which of the following? [I is the identity matrix of order 2] Option 1: (a^2+ab+1)I - bA Option 2: (b^2+ab-1)I - aA Option 3: (a^2+bc+1)I - bA Option 4: (a^2+bc+1)I - aA

Answer: (a^2+bc+1)I - aA. Solution: A, = a*(1+bc)/a - bc = 1, so A^(-1) = adjA = bmatrix (1+bc)/a & -b \\ -c & a bmatrix and aA^(-1) = bmatrix 1+bc & -ab \\ -ac & a^2 bmatrix. Expanding (a^2+bc+1)I - aA gives exactly this matrix.

Algebra

Matrices & Determinants

Hard

common

If $A = \begin{bmatrix} a & b \\ c & \frac{1+bc}{a} \end{bmatrix}$ , then $aA^{-1}$ is equal to which of the following? [I is the identity matrix of order 2]

$(a^2+ab+1)I - bA$

$(b^2+ab-1)I - aA$

$(a^2+bc+1)I - bA$

$(a^2+bc+1)I - aA$

✅ Correct Option: 4

$|A| = a\cdot\frac{1+bc}{a} - bc = 1$ , so $A^{-1} = \text{adj}A = \begin{bmatrix} \frac{1+bc}{a} & -b \\ -c & a \end{bmatrix}$ and $aA^{-1} = \begin{bmatrix} 1+bc & -ab \\ -ac & a^2 \end{bmatrix}$ . Expanding $(a^2+bc+1)I - aA$ gives exactly this matrix.

2026: 18 May Shift 1

For what values of $x$ and $y$ , are the following matrices equal?

$A=\begin{bmatrix}2x+1 & 3y\\ 0 & y^2-5y\end{bmatrix}$ , $B=\begin{bmatrix}x+3 & y^2+2\\ 0 & -6\end{bmatrix}$

2025: 3 June Shift 1

Let A be a matrix such that $A = \begin{bmatrix} 1 & 2 \\ -2 & 3 \end{bmatrix}$ . Then which of the following are TRUE?

(A) A is non-singular matrix

(B) $A^T = A$

(D) A is not skew-symmetric matrix

Choose the correct answer from the options given below:

2025: 21 May Shift 1

If $\begin{bmatrix} x-y & t \\ 2x-y & w \end{bmatrix} = \begin{bmatrix} -1 & 2 \\ 0 & 1 \end{bmatrix}$ , then $2x + y + 3t + w$ is equal to

2026: 21 May Shift 1

Which of the following matrices are invertible?

(A) $\begin{bmatrix} 2 & 2 \\ 3 & 3 \end{bmatrix}$

(B) $\begin{bmatrix} 2 & 3 \\ 3 & 2 \end{bmatrix}$

(D) $\begin{bmatrix} 3 & 3 \\ 3 & 3 \end{bmatrix}$

Choose the correct answer from the options given below:

2025: 16 May Shift 1

If A and B are square matrices of order 3 such that |A| = -1 and |B| = 5, then the value of |3AB| is

2026: 29 May Shift 2

Let $A=[a_{ij}]_{3\times3}$ , where $a_{ij}=i-j$ , then which of the following statements is/are TRUE ?

A. A is diagonal matrix

B. A is square matrix

C. A is symmetric matrix

D. A is skew symmetric matrix

Choose the correct answer from the options given below:

If A=[abc1+bca]A = \begin{bmatrix} a & b \\ c & \frac{1+bc}{a} \end{bmatrix}A=[ac​ba1+bc​​], then aA−1aA^{-1}aA−1 is equal to which of the following? [I is the identity matrix of order 2]

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

If $A = \begin{bmatrix} a & b \\ c & \frac{1+bc}{a} \end{bmatrix}$ , then $aA^{-1}$ is equal to which of the following? [I is the identity matrix of order 2]