If for a matrix A, A=`A^(-1)`, then show that
`A(A^(3)+I)=A+I` (I is the unit matrix).

If for a matrix A , A^5=I , then A^-1=

If A be a 2 times 2 matrix such that A^(2)=A , then show that (I-A)^(2)=I-A where I is the unit matrix of order 2 times 2 .

If A = [[2,2],[4,3]] show that A A^(-1) = I_2 where I_2 is the unit matrix of order 2.

If A = [(4,5),(5,6)] show that, A^(2) = 10A + I where I is the unit matrix or order 2. Hence, find the inverse of A.

If A=\begin{bmatrix} 1 & 2 & 2\\ 2 & 1 & 2\\ 2 & 2 & 1 \end{bmatrix} , then show that A^2-4A-5I=O ,where I and 0 are the unit matrix and the null matrix of order 3, respectively. Use this result to find A^(-1)dot

If A is a matrix of order n such that A^(T)A=I and X is any matrix such that X=(A+I)^(-1) (A-I) , then show that X is skew symmetric matrix.

If A = [[4,5],[5,6]] , show that A^2 = 10A + I where I is the unit matrix of order 2.

If A = [(2,2),(4,3)] show that, A A^(-1) =I_(2) wher I_(2) is the unit matrix of order 2.

If A is a square matrix such that A^2=A , then write the value of 7A-(I+A)^3, where I is the identity matrix.

If A = [(4,1),(7,2)] find a matrix B such that AB = I where I is the unit matrix of order 2.