# JEE Main & Advanced Mathematics Matrices Positive Integral Powers of a Matrix

## Positive Integral Powers of a Matrix

Category : JEE Main & Advanced

The positive integral powers of a matrix A are defined only when A is a square matrix.

Also then ${{A}^{2}}=A.A$, ${{A}^{3}}=A.A.A={{A}^{2}}A$.

Also for any positive integers $m$ and $n,$

(i) ${{A}^{m}}{{A}^{n}}={{A}^{m+n}}$

(ii) ${{({{A}^{m}})}^{n}}={{A}^{mn}}={{({{A}^{n}})}^{m}}$

(iii) ${{I}^{n}}=I,{{I}^{m}}=I$

(iv) ${{A}^{0}}={{I}_{n}}$, where A is a square matrix of order $n$.

LIMITED OFFER HURRY UP! OFFER AVAILABLE ON ALL MATERIAL TILL TODAY ONLY!

You need to login to perform this action.
You will be redirected in 3 sec