with(LinearAlgebra): A := Matrix(3,[[1, 0, -1],[-1,2,0],[0,1,1]]);

NiM+SSJBRzYiLUknUlRBQkxFR0YlNiUiKV9ZPj8tSSdNQVRSSVhHRiU2IzclNyUiIiIiIiEhIiI3JUYxIiIjRjA3JUYwRi9GL0knTWF0cml4RzYkSSpwcm90ZWN0ZWRHRjdJKF9zeXNsaWJHRiU=

B := Matrix(3,[[-1, 1, 0],[3,0,2],[1,1,1]]);

NiM+SSJCRzYiLUknUlRBQkxFR0YlNiUiJyUzVyktSSdNQVRSSVhHRiU2IzclNyUhIiIiIiIiIiE3JSIiJEYxIiIjNyVGMEYwRjBJJ01hdHJpeEc2JEkqcHJvdGVjdGVkR0Y4SShfc3lzbGliR0Yl

A.B;

NiMtSSdSVEFCTEVHNiI2JSIpQyU+JD4tSSdNQVRSSVhHRiU2IzclNyUhIiMiIiEhIiI3JSIiKEYvIiIlNyVGMiIiIiIiJEknTWF0cml4RzYkSSpwcm90ZWN0ZWRHRjhJKF9zeXNsaWJHRiU=

B.A;

NiMtSSdSVEFCTEVHNiI2JSIpUzlPPy1JJ01BVFJJWEdGJTYjNyU3JSEiIyIiIyIiIjclIiIkRi4hIiI3JSIiIUYxRjRJJ01hdHJpeEc2JEkqcHJvdGVjdGVkR0Y3SShfc3lzbGliR0Yl

C:= Matrix(3,[[1, 0, -1],[3,2,4],[-2,1,0]]);

NiM+SSJDRzYiLUknUlRBQkxFR0YlNiUiKUcxUD8tSSdNQVRSSVhHRiU2IzclNyUiIiIiIiEhIiI3JSIiJCIiIyIiJTclISIjRi9GMEknTWF0cml4RzYkSSpwcm90ZWN0ZWRHRjpJKF9zeXNsaWJHRiU=

MatrixInverse(C);

NiMtSSdSVEFCTEVHNiI2JSIpb1dWPy1JJ01BVFJJWEdGJTYjNyU3JSMiIiUiIzYjIiIiRi8jISIjRi83JSMiIilGLyMiIiNGLyMiIihGLzclIyEiKEYvRjBGMkknTWF0cml4RzYkSSpwcm90ZWN0ZWRHRkBJKF9zeXNsaWJHRiU=

Determinant(C);

NiMhIzY=

r1 := Matrix(3,[[cos(t), -sin(t), 0],[sin(t),cos(t),0],[0,0,1]]);

NiM+SSNyMUc2Ii1JJ1JUQUJMRUdGJTYlIigrI282LUknTUFUUklYR0YlNiM3JTclLUkkY29zRzYkSSpwcm90ZWN0ZWRHRjJJKF9zeXNsaWJHRiU2I0kidEdGJSwkLUkkc2luR0YxRjQhIiIiIiE3JUY3Ri9GOjclRjpGOiIiIkknTWF0cml4R0Yx

r2 := Matrix(3,[[cos(t), sin(t), 0],[-sin(t),cos(t),0],[0,0,1]]);

NiM+SSNyMkc2Ii1JJ1JUQUJMRUdGJTYlIilLMl0/LUknTUFUUklYR0YlNiM3JTclLUkkY29zRzYkSSpwcm90ZWN0ZWRHRjJJKF9zeXNsaWJHRiU2I0kidEdGJS1JJHNpbkdGMUY0IiIhNyUsJEY2ISIiRi9GODclRjhGOCIiIkknTWF0cml4R0Yx

r2.r1;

NiMtSSdSVEFCTEVHNiI2JSIpW1dfPy1JJ01BVFJJWEdGJTYjNyU3JSwmKiQtSSRjb3NHNiRJKnByb3RlY3RlZEdGMkkoX3N5c2xpYkdGJTYjSSJ0R0YlIiIjIiIiKiQtSSRzaW5HRjFGNEY2RjciIiFGOzclRjtGLUY7NyVGO0Y7RjdJJ01hdHJpeEdGMQ==

cc := Matrix(3, [[0.5, 0.5*2^0.5, 0.5], [0.5*2^0.5, 0,-0.5*2^0.5], [0.5, -0.5*2^0.5, 0.5]]);

NiM+SSNjY0c2Ii1JJ1JUQUJMRUdGJTYlIilXIVEwIy1JJ01BVFJJWEdGJTYjNyU3JSQiIiYhIiIkIis1eTFycSEjNUYvNyVGMiIiISQhKzV5MXJxRjQ3JUYvRjdGL0knTWF0cml4RzYkSSpwcm90ZWN0ZWRHRjxJKF9zeXNsaWJHRiU=

MatrixInverse (cc);

NiMtSSdSVEFCTEVHNiI2JSIpITNxMCMtSSdNQVRSSVhHRiU2IzclNyUkIjMrKysrKysrK10hIz0kIjM9XTR0OHkxcnFGL0YtNyVGMCQiIiFGNCQhMz1dNHQ4eTFycUYvNyVGLUY1Ri1JJ01hdHJpeEc2JEkqcHJvdGVjdGVkR0Y6SShfc3lzbGliR0Yl

Determinant(cc);

NiMkISskKioqKioqKioqISM1

ab := Matrix(3, [[a-E, b, 0], [b, a-E,b], [0, b, a-E]]);

NiM+SSNhYkc2Ii1JJ1JUQUJMRUdGJTYlIilDRSQ0Iy1JJ01BVFJJWEdGJTYjNyU3JSwmSSJhR0YlIiIiSSJFR0YlISIiSSJiR0YlIiIhNyVGNEYvRjQ3JUY1RjRGL0knTWF0cml4RzYkSSpwcm90ZWN0ZWRHRjpJKF9zeXNsaWJHRiU=

cc.ab.cc;

NiMtSSdSVEFCTEVHNiI2JSIpYzkpNCMtSSdNQVRSSVhHRiU2IzclNyUsKEkiYUdGJSQiKygqKioqKioqKiohIzVJIkVHRiUkISsoKioqKioqKioqRjFJImJHRiUkIitpTkA5OSEiKiQiIiFGOiwmRi4kIiIkRjFGMiQhIiRGMTclRjksJkYuJCIrJSoqKioqKioqKkYxRjIkISslKioqKioqKioqRjFGOTclRjtGOSwoRi5GL0YyRjNGNSQhK2lOQDk5RjhJJ01hdHJpeEc2JEkqcHJvdGVjdGVkR0ZMSShfc3lzbGliR0Yl