If `A=[[1,3,3],[3,1,3],[3,3,1]]`prove that `A^2-5A`is a scalar matrix.

If A=[[5,-3],[4,-3],[-2,1]] ,prove that (A^T)^T=A

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

Answer the following questions.If A=[[1,2],[3,2],[-1,0]] and B=[[,1,3,2],[4,-1,-3]] ,show that AB is singular matrix.

If A=[[-1,2,1],[-3,2,-3]] and B=[[2,1],[-3,2],[-1,3]] , prove that (A+B^T)^T=A^T+B

Transform [[1,-1,2],[2,1,3],[3,2,4]] into an upper triangular matrix by suitable row transformations

Find the inverse of the matrix [[2,1,3],[4,-1,0],[-7,2,1]] by using Adjoint of a matrix.

Find the inverse of A=[[1,3,3],[1,4,3],[1,3,4]] and B = [[1,2,3],[1,1,5],[2,4,7]] then, find a matrix X such that XA = B .

If A = [[1,0,1],[0,2,3],[1,2,1]] and B = [[1,2,3],[1,1,5],[2,4,7]] , then find a matrix X such that XA = B .