Matrices and transformations questions | form four Basic Mathematics

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#	Question
1	Find the inverse and identity matrix of $A=egin{pmatrix} 6 &4 \ -2 & 5 end{pmatrix}$ . Mathematical Calculation
2	Triangle OAB has vertices at O(0,0), A(2,1) and B(-1,3). If the triangle is enlarged by $E=egin{pmatrix} 2 & 0\ 0 & 2 end{pmatrix}$ nd then translated by $T=inom{-3}{-5}$ , Find the vertices of the triangle. Draw on the same x - y plane triangle OAB and the images after being: (i)enlarged (ii)translated Mathematical Calculation
3	Given matrices $A=egin{pmatrix} 3 & 5 \ 4 & -2 end{pmatrix}$ , $B=egin{pmatrix} 3 & -1 \ -3 & 2 end{pmatrix}$ and $C=egin{pmatrix} k & -4 \ 3 & -2 end{pmatrix}$ : Find A²+2A Find t and y such that B²=tB+yI where I is an identity matrix. Find the value of k if the determinant of C is 5. Mathematical Calculation
4	A linear translation Q carried point (x,y) into (x`,y`) such that x`=5x-3y and y`=-2x+4y. Determine the transformation matrix Q . Find Q(3,3). Find the image of the point obtained in part (ii) under Q. Mathematical Calculation
5	If A and B are square matrices of order 2x2, expand the brackets for (A+B)(A-B). Mathematical Calculation
6	Work out the values of x and y in the following cases: $egin{pmatrix} 5 & 7\ 6 & 8 end{pmatrix}inom{2}{3}=inom{x}{y}$ $egin{pmatrix} 6 & 4\ 8 & 10 end{pmatrix}inom{x}{y}=inom{24}{46}$ Mathematical Calculation
7	Find the equation of the line joining points (1,7) and (2,9) after a reflection in the line y=x. Mathematical Calculation
8	Find the inverse of matrix $A=egin{pmatrix} 2 & -3\ 1 & 2 end{pmatrix}$ . Find the point P(x,y) if $A=egin{pmatrix} 2 & -3\ 1 & 2 end{pmatrix}inom{x}{y}=inom{-5}{8}$ . Determine the image of the point obtained in part (b) under enlargement by the matrix $egin{pmatrix} 2 & 0\ 0 & 2 end{pmatrix}$ followed by a reflection in the line y=x. Mathematical Calculation
9	Determine a matrix M which represents a reflection in the line y−x=0. Find the image of the line x+2y-4=0 after a reflection in the line y-x=0. Mathematical Calculation
10	If $A=egin{pmatrix} 3 & 2\ 4 & -1 end{pmatrix}$ find \|A\| and A^-1. Use the inverse matrix obtained in (i) to solve 3x+2y=12 and 4x-y=5. Mathematical Calculation