Question

If A is involutary then$\left|A\right|=1or-1$

• A. True
• B. False

Answer 1

The correct option is A

True

We know that for a matrix A to be called as involutery $A^2$ should be equal to I

$A^2=I$

$So|A\wedge 2|=\left|I\right|{\left|A\right|}^2=1\left(asdeterminantofidentitymatrixis1\right).Also{\left|A\right|}^2=\left|A\right|={\left|A\right|}^2(Refertotheofdeterminantswhichsaysthat\left|AB\right|=\left|A\right|\left|B\right|).HereAandBaresameonly)So\left|A\right|=1or-1.$