Question

If A is a square matrix such that $A^2=I$ where I is the identity matrix, then what is $A^{-1}$ equal to ?

• A. A + 1
• B. Null matrix
• C. A
• D. Transpose of A

Answer 1

Answer: (C)

A

$A\to$square matrix

$A^2=I$

To find $A^{-1}=?$

Given $A^2=I$

$\Rightarrow A\times A=I$

$\Rightarrow A=\frac{I}{A}$

$\Rightarrow A=A^{-1}$

$\therefore A^{-1}=A$

Option C is correct