Question-7

Select all idempotent matrices from the options given below.

• \(\begin{bmatrix}3 & -6\\1 & -2\end{bmatrix}\)

• \(\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}\)

• \(\begin{bmatrix}2 & -2\\1 & -1\end{bmatrix}\)

• \(\begin{bmatrix}3 & 1\\-1 & 2\end{bmatrix}\)

Answer

• \(\begin{bmatrix}3 & -6\\1 & -2\end{bmatrix}\)

• \(\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}\)

• \(\begin{bmatrix}2 & -2\\1 & -1\end{bmatrix}\)

• \(\begin{bmatrix}3 & 1\\-1 & 2\end{bmatrix}\)

Solution

A matrix \(A\) is idempotent if \(A^2 = A\). Of the four matrices given here, exactly two of them are idempotent.