Q12 of 127 Page 122

Let . Verify that (AB)^–1 = B^–1 A^–1.

We have AB = = (61)(67)-(47)(87) = -2

Here determinant of matrix = |AB|≠ 0 hence (AB)^-1 exists.

Also |A| = 1 ≠ 0 and |B| = -2 ≠ 0.

∴ A^-1 and B^-1 will also exist and are given by-

And hence,

{Hence proved}

Find the inverse of each of the matrices (if it exists)

If , show that A² – 5A + 7I = O. Hence find A^–1.

For the matrix , find the numbers a and b such that A² + aA + bI = O.

Let . Verify that (AB)–1 = B–1 A–1.