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PreUniversity Mathematics  Matrices1. For the square matrix show that A (adj A) = AI 2. Find the inverse of 3.If and , find B. 4. If show that A is an orthogonal, that is . 5. Find the inverse of 6. Given two matrices where and , verify . 7. Using matrices, solve the equations x+y+2z = 4 2xy+3z = 9 3xyz=2. 8. If the matrix A is fiven by , prove that it satisfies the relation where I stands for the unit matrix of order 2. 9. If and , prove that . 10.Express as the sum of a symmetric and skew symmetric matrices. A symmetric matrix is a square matrix if (i,j)th element of A is equal to (j,i)th element of A. A skew symmetric matric is a square matrix if the (i,j)th element of A is equal to the negative of the (j,i)th element of A. Character is who you are when no one is looking. 