If `A=[[1,0],[-1,7]]`find k so that `A^2-8A-kI=O`,where I is a unit matrix and O is a null matrix of oreder 2.

If A=[[3,1],[-1,2]] prove that A^2-5A+7I=O ,where I is unit matrix of order 2.

If A=[[1,-2],[5,6]],B=[[3,-1],[3,7]] ,Find AB-2I ,where I is unit martrix of order 2.

If A=[[1,-2],[5,3]],B=[[1,-3],[4,-7]] ,then find the matrix A-2B+6I , where I is the unit matrix of order 2.

If A=[[5,4],[-2,3]] and B=[[-1,3],[4,-1]] ,then find C^T such that 3A-2B+C=I ,where I is the unit matrix of order 2.

If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] ,show that A^TA=I ,where I is the unit matrix of order 2.

Select the correct options from the given alternatives:If A=[[1,2,2],[2,1,-2],[a,2,b]] is a matrix satisfying the equation A.A^T=9I ,where I is the identity matrix of order 3,then the paired (a,b) is equal to