If A=[0&1 0&0], I is the unit matrix of order 2 and a, b are arbitrary constants, then (aI + bA)2 is equal to

Question

If A=[0&1 0&0], I is the unit matrix of order 2 and a, b are arbitrary constants, then (aI + bA)2 is equal to (A) a2I + abA (B) a2I + 2abA (C) a2I + b2A (D) None of these

Tardigrade Admin · Accepted Answer

(aI+bA)2=a2I2+b2A2+2ab AI =a2I2+b2 A2+2abA But A2=[0&0 0&0] ∴ (aI+bA)2=a2I+2abA.

Q. If $A = [0010]$ , I is the unit matrix of order 2 and a, b are arbitrary constants, then $(a I + b A)^{2}$ is equal to

$a^{2} I + ab A$

$a^{2} I + 2 ab A$

$a^{2} I + b^{2} A$

None of these

$(a I + b A)^{2} = a^{2} I^{2} + b^{2} A^{2} + 2 ab A I$
$= a^{2} I^{2} + b^{2} A^{2} + 2 ab A$
But $A^{2} = [0000] ∴ (a I + b A)^{2} = a^{2} I + 2 ab A .$

Q. If A=[00​10​], I is the unit matrix of order 2 and a, b are arbitrary constants, then (aI+bA)2 is equal to

a2I+abA

a2I+2abA

a2I+b2A