Question

Let A $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and B = $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ are two matrices such that AB = BA and c ¹ 0, then value of $\frac{a - d}{3b - c}$ is

• A. 0
• B. 2
• C. –2
• D. – 1

Answer 1

Answer: (D)

– 1

Answer 2

AB = $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$= $\begin{bmatrix} a + 2c & b + 2d \\ 3a + 4c & 2c + 4d \end{bmatrix}$

BA = $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$= $\begin{bmatrix} a + 3b & 2a + 4b \\ c + 3d & 2c + 4d \end{bmatrix}$

if AB = BA, then a + 2c = a + 3b

̃ 2c = 3b ̃ b ¹ 0

b + 2d = 2a + 4b

̃ 2a – 2d = – 3b

$\frac{a - d}{3b - c} = \frac{- \frac{3}{2}b}{3b - \frac{3}{2}b}$= – 1