`" If matrix "A" and "B" are such that "AB=BA" and "A+B=1" ,then the matrix "A^(3)+B^(3)" is equal to "`

If A is matrix of order 3 such that |A|=5 and B= adj A, then the value of ||A^(-1)|(AB)^(T)| is equal to (where |A| denotes determinant of matrix A. A^(T) denotes transpose of matrix A, A^(-1) denotes inverse of matrix A. adj A denotes adjoint of matrix A)

The number of n xx n matrix A and B such that AB-BA=I is.

The number of n xx n matrix A and B such that AB-BA=I is.

" For the matrix A and identity matrix "I," if "AB=BA=I" then that matrix "B" is inverse matrix and "A" is invertible "A^-1=

Let A be an orthogonal matrix, and B is a matrix such that AB=BA , then show that AB^(T)=B^(T)A .

If A is a 3 xx 3 non-singular matrix such that A A^(T) = A^(T)A " and "B = A^(-1)A^(T), " then "B B^(T) is equal to

Let A and B are square matrices of order 3 such that AB^(2)=BA and BA^(2)=AB . If (AB)^(2)=A^(3)B^(n) , then m is equal to