If , show that A2 = A.

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

If $A = [\begin{array}{ccc} 2 & - 2 & - 4 \\ - 1 & 3 & 4 \\ 1 & - 2 & - 3 \end{array}]$ , show that A² = A.

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Given : $A = [\begin{array}{ccc} 2 & - 2 & - 4 \\ - 1 & 3 & 4 \\ 1 & - 2 & - 3 \end{array}]$ ......(1)

$A^{2} = A \cdot A = [\begin{array}{ccc} 2 & - 2 & - 4 \\ - 1 & 3 & 4 \\ 1 & - 2 & - 3 \end{array}] \cdot [\begin{array}{ccc} 2 & - 2 & - 4 \\ - 1 & - 3 & 4 \\ 1 & - 2 & - 3 \end{array}]$

$= [\begin{array}{ccc} 4 + 2 - 4 & - 4 - 6 + 8 & - 8 - 8 + 12 \\ - 2 - 3 + 4 & 2 + 9 - 8 & 4 + 12 - 12 \\ 2 + 2 - 3 & - 2 - 6 + 6 & - 4 - 8 + 9 \end{array}]$

$= [\begin{array}{ccc} 2 & - 2 & - 4 \\ - 1 & 3 & 4 \\ 1 & - 2 & - 3 \end{array}]$ ....(2)

from (1) & (2) we can say that

A² = A