Question

If A =$\begin{bmatrix} 1 & tanx \

• tanx & 1 \end{bmatrix}$, then the value of |A^TA⁻¹| is

• A. cos4x
• B. sec²x
• C. − cos4x
• D. 1

Answer 1

Answer: (D)

1

Answer 2

A^T = $\begin{bmatrix} 1 & - \tan x \\ \tan x & 1 \end{bmatrix}$

A⁻¹ = $\frac { 1 } { 1 + \tan ^ { 2 } x }$ $\begin{bmatrix} 1 & - \tan x \\ \tan x & 1 \end{bmatrix}$

A^TA⁻¹ = $\begin{bmatrix} \cos 2x & - \sin 2x \\ \sin 2x & \cos 2x \end{bmatrix}$

| A^TA⁻¹| = 1