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What's the Square matrix A equal to if a = a^2 ?

Last Updated on Wednesday 5th Oct 2022

matrix a^2

Such a matrix is called idempotent.

Idempotent matrix

In linear algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself.That is, the matrix A is idempotent if and only if A2 = A

matrix a^2 = a

Examples of 2 × 2 idempotent matrices

\begin{bmatrix}1 \ 1\\2 \ 3\end{bmatrix}\begin{bmatrix}3 \ 5 \\8 \ 1\end{bmatrix}

a 2 a matrix

matrix squared equals itself