❖ In the lesson, we have explained the Powers of a matrix.

❖ The power \(A^n\) of a matrix \(A\) for n a nonnegative integer \(n\) is defined as the matrix product of \(n\) copies of \(A\), where \(A\) is a square matrix (for example the size of \(A\) can be \(2 \times 2\), \(3 \times 3\), and so on).

\(A^0\) is defined to be the identity matrix of the same size, where \(A^0=I_n\) ( \(I_n\) is \(n \times n\) an identity matrix with the same size as \(A\)).

❖ The number of rows and columns that a matrix has is called its size, its order, or its dimension.