Question

The number of solutions of the matrix equation

A² = $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ is –

• A. 2
• B. 4
• C. 8
• D. Infinitely many

Answer 1

Answer: (D)

Infinitely many

Answer 2

A = ±I, $\pm \begin{bmatrix} 1 & 0 \\ c & - 1 \end{bmatrix}$, $\begin{bmatrix} 1 & b \\ \frac{1}{b} & 0 \end{bmatrix}$, $\begin{bmatrix} a & b \\ \frac{1 - a^{2}}{b} & - a \end{bmatrix}$

where a, b, c are arbitrary and h ¹ 0.