If A =    show that A² = A^-1

Find the angle between the lines x−5/2​=y−5/1​=−z+1/-1​ and x/3​=y−1​/2=z+5/3​.

If a=5i^−j^​−3k^ and b=i^−3j^​−5k^, show that a+b and a−b are perpendicular to each other.

 Evaluate the integral ∫ e^x(e^x+7)⁵dx.

If y=ax+b/x​, show that x²  d²y/dx²​+x dy/dx​−y=0

If α and β are roots of x²−3ax+a²=0 and α2+β²=9/7​, find the value of a.

Use the principle of mathematical induction to show that 1+3+5+ -------- + (2n -1) = n²  for each n∈N.

If A = [2 -1 3] and B=  check

Whether AB = BA.

 Snow that  

Shunyavada

Cynicism

 Thales

Aranyakas

Rationalism

Videha-Mukti

Lokayata

Stoic Ethics

What is Aristotle's philosophy of God?

What is Parmenides' concept of Being?

What is the ethical principle of Pythagoras?